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Краткий гайд по квантованию нейросетей

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Мы достаточно написали статей про оптимизацию ваших нейросетей, сегодня пора перейти к дроблению, уменьшению и прямому урезанию, иначе квантованию данных. Сам по себе процесс этот несложный с точки зрения всего, но подводные камни у операции есть.

Мы буквально уменьшаем битность данных, что позволяет сократить вычислительные ресурсы и уменьшить объем памяти, необходимой для хранения моделей.

Наша карточка от Nvidia пользуется дешевыми, например, 8-битными ядрами для вычисления операций свертки/умножения матриц - мы получаем дешевую модель. Конечно, такое подрезание чисел с плавающей запятой может приводить и к снижению точности. Катастрофической.

Придумали разные методы квантования, каждый из которых имеет свои особенности, подходы и применения.

Их делят по трем критериям: униформное и неуниформное квантование, симметричное и асимметричное квантование, а также статическое и динамическое квантование. Углубляться мы не будем. Главное, что квантование может приводиться не только к 8-битности, но и к 16...

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Там, где данные с высокой массой распределения от -1 до 1 - там вероятно значение входит в диапазон. Самое главное - квантование - это всегда приближение, которое может обходиться вам дороговато. Если вы решили сократить объем память в несколько раз и буквально перевести float32 к int8, особенно... Т.е от плавающей запятой к целочисленным значениям.

Если все плохо, то приводится, например, статическое квантование. Иначе, модель сразу обучается на "квантованных" данных.

Два принципа квантования

Практическая реализация идет, например, через Post-training quantization (PTQ) и базируется на постобучающем преобразовании модели, уже завершившей тренировку на данных с высокой точностью чисел, обычно 32-битных с плавающей запятой. Тот случай, когда мы рассчитываем, что наша супермодель выживет от такого удешевления данных.

Поэтому основная цель PTQ — минимизировать потребление памяти и вычислительных ресурсов на этапе инференса без необходимости повторного обучения модели.

В PTQ веса модели и, в некоторых случаях, активации преобразуются в целочисленные значения меньшей разрядности, чаще всего это 8-битные целые числа (int8), что позволяет существенно сократить размер модели и ускорить вычисления за счёт использования инструкций SIMD (Single Instruction, Multiple Data) на уровне аппаратного обеспечения.

SIMD-операции обрабатывают несколько данных с помощью одной инструкции. В этом их отличие от традиционных/скалярных операций.

В PTQ не происходит изменений в архитектуре нейронной сети, и алгоритм квантования выполняется отдельно от процесса обучения.

Основные этапы включают квантование весов с плавающей запятой в int8 посредством вычисления масштабов и нулевых сдвигов, что позволяет сохранить диапазон значений. Это осуществляется с помощью статистической информации, собранной на небольшом объёме тренировочных данных.

Важно, что через PTQ активации и веса могут квантоваться по-разному: активации могут квантоваться динамически на этапе инференса в зависимости от входных данных, тогда как веса — статически на основе априорной (изначальной) статистики.

Если вы действительно работаете над глубокой-глубокой нейросетью, то могут возникнуть проблемы с точностью, то же относится к задачам с высокой чувствительностью в данных.

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Quantization-Aware Training (QAT) сложнее - тут квантование учитывается уже на этапе обучения модели.

В отличие от PTQ, в QAT веса и активации модели представляются в формате низкой разрядности (int8 или int16) в ходе всего процесса тренировки, что позволяет модели адаптироваться к ограниченной точности чисел.

Архитектура QAT предполагает, что квантованные версии весов используются не напрямую, а через эмуляцию процесса квантования во время прямого и обратного прохода модели.

В прямом проходе веса и активации моделируются как квантованные целые числа, что позволяет эффективно эмулировать процесс инференса в квантованной среде. Обратный проход, однако, используется с весами с плавающей запятой, что сохраняет точность градиентного спуска и позволяет корректировать модель в условиях ограниченной точности.

В процессе обучения модель "учится" компенсировать ошибки, вызванные квантованием, что позволяет снизить потери точности, наблюдаемые при PTQ. QAT требует значительно большего объёма вычислительных ресурсов на этапе обучения, так как тренировка должна учитывать квантование всех промежуточных активаций и весов.

При этом необходимо выполнять симуляцию квантования не только для весов, но и для входных данных на каждом слое, что увеличивает вычислительную сложность модели на этапе тренировки.

Для реализации QAT требуется модификация стандартных слоёв нейронной сети таким образом, чтобы они поддерживали низкоразрядные вычисления, а также корректная настройка механизмов обратного распространения ошибки.

Применение QAT часто связано с такими задачами, как развёртывание на мобильных устройствах, где вычислительные ресурсы и память ограничены. Поэтому частенько такая архитектура квантования применяется для задач CV, когда мы ставим камеру с микропроцессором и ждем чуда детекции...

Как все это работает на практике?

В TensorFlow квантование реализовано через TensorFlow Lite — облегчённую версию TensorFlow, специально предназначенную для развертывания моделей на устройствах с ограниченными ресурсами, ну там raspberry pi)))

PTQ в TensorFlow Lite можно выполнить через использование метода post-training quantization, где модель, обученная с плавающей запятой, автоматически конвертируется в квантованную версию с помощью функции converter.optimizations = [tf.lite.Optimize.DEFAULT].

Этот процесс включает статическое квантование весов с помощью небольшого набора калибровочных данных для расчёта масштабов и сдвигов нулевого уровня. Пример кода в TensorFlow Lite для PTQ может выглядеть следующим образом:

import tensorflow as tf

# Загрузка модели
model = tf.keras.models.load_model('model.h5')

# Конвертация модели с использованием PTQ
converter = tf.lite.TFLiteConverter.from_keras_model(model)
converter.optimizations = [tf.lite.Optimize.DEFAULT]
tflite_model = converter.convert()

# Сохранение квантованной модели
with open('model_quantized.tflite', 'wb') as f:
    f.write(tflite_model)

Для сложного сценария квантования QAT в TensorFlow применяется функционал встроенного квантования на этапе тренировки, который позволяет учитывать квантованные представления весов и активаций в процессе обучения.

Все идет через tf.quantization.fake_quant_with_min_max_vars, где происходит симуляция квантования в прямом и обратном проходах.

Однако это требует более детальной настройки сети и специфических изменений в процессе тренировки.

В PyTorch квантование поддерживается через пакет torch.quantization, который позволяет как пост-тренировочное квантование, так и QAT.

В PyTorch модульны подход, позволяющий кодерам выбирать между симметричным, асимметричным квантованием, а также реализовывать как динамическое квантование активаций, так и статическое квантование весов.

Перед тем как провести квантование по PTQ в PyTorch включают подготовку модели через функции torch.quantization.prepare() и преобразование через torch.quantization.convert().

Пример кода для PTQ в PyTorch:

import torch
import torch.quantization

# Загрузка обученной модели
model = MyPretrainedModel()

# Подготовка модели к квантованию
model.eval()
model.qconfig = torch.quantization.get_default_qconfig('fbgemm')
torch.quantization.prepare(model, inplace=True)

# Применение PTQ
torch.quantization.convert(model, inplace=True)

# Тестирование квантованной модели
output = model(input_data)

Для QAT в PyTorch используется аналогичная структура, но с добавлением процедуры обучения с учётом квантования.

Модель сначала подготовлена через torch.quantization.prepare_qat(), и затем продолжается обучение, при котором происходит симуляция квантования.

Важно отметить, что во время обучения модель работает с весами с плавающей запятой, однако на этапе инференса она конвертируется в int8.

ONNX (Open Neural Network Exchange) — это открытый формат для представления моделей глубокого обучения, который обеспечивает переносимость моделей между разными фреймворками.

Для квантования в ONNX используется onnxruntime, поддерживающий как статическое, так и динамическое квантование.

Статическое квантование в ONNX работает через калибровочные данные - они используются для вычисления квантованных значений до начала инференса, в то время как динамическое квантование применяется только к весам, что упрощает процесс и снижает нагрузку на инференс.

Пример квантования модели в ONNX может выглядеть следующим образом:

import onnx from onnxruntime.quantization import quantize_dynamic, QuantType

model_fp32 = 'model.onnx' model_quant = 'model_quant.onnx'

Квантование с дистилляцией и прунингом

Часто процесс квантования проводится совместно с другими методами оптимизация - тем же прунингом или дистилляцией.

Pruning - это метод, при котором ненужные или малоактивные нейроны и связи удаляются из сети без существенного ущерба для её производительности.

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Прореживание может быть выполнено на основе различных критериев, таких как величина весов (weights magnitude pruning), где удаляются веса, чьи значения минимальны, или на основе анализа чувствительности (sensitivity analysis pruning), где оценивается вклад каждого нейрона в общую ошибку модели.

В сочетании с квантованием pruning может значительно сократить количество вычислений, так как после прореживания остаются лишь активные нейроны, на которых квантование может быть применено.

Например, после выполнения pruning модель может быть преобразована в квантованную версию с меньшим числом параметров, что ещё больше снижает её вычислительную сложность.

Практическая реализация pruning с последующим квантованием в TensorFlow может выглядеть следующим образом:

import tensorflow_model_optimization as tfmot


model = tf.keras.models.load_model('model.h5')


prune_low_magnitude = tfmot.sparsity.keras.prune_low_magnitude
pruned_model = prune_low_magnitude(model)


pruned_model.compile(optimizer='adam', loss='sparse_categorical_crossentropy')
pruned_model.fit(train_data, train_labels, epochs=2)


converter = tf.lite.TFLiteConverter.from_keras_model(pruned_model)
converter.optimizations = [tf.lite.Optimize.DEFAULT]
tflite_quantized_model = converter.convert()


with open('model_pruned_quantized.tflite', 'wb') as f:
    f.write(tflite_quantized_model)

По порядку.

Сначала мы загружаем модель с помощью tf.keras.models.load_model('model.h5').

Эта модель может быть предварительно обученной нейронной сетью, например, для задачи классификации изображений или распознавания речи.

Для прореживания модели используется метод prune_low_magnitude, который является частью библиотеки tensorflow_model_optimization.

Метод удаляет связи (нейронные веса), значения которых близки к нулю, тем самым уменьшая размер модели и снижая объём вычислений, которые она требует.

В результате создаётся версия модели pruned_model, в которой часть параметров обнуляется. Это помогает сократить сложность модели и ускорить её выполнение без значительной потери точности.

После применения метода прореживания модель компилируется и дообучается на тренировочных данных с помощью метода fit(). Это необходимо для того, чтобы модель адаптировалась к изменённой структуре, где часть нейронных связей была удалена.

После завершения обучения модель подвергается пост-тренировочному квантованию с помощью TFLiteConverter.

Этот процесс заключается в преобразовании весов модели из 32-битного представления (FP32) в 8-битное целочисленное (int8), что значительно сокращает объём памяти, занимаемой моделью, и ускоряет инференс.

При этом используются оптимизации, заданные через converter.optimizations = [tf.lite.Optimize.DEFAULT]. После этого модель сохраняется в формате TFLite, что позволяет её легко развернуть на устройствах с ограниченными вычислительными ресурсами, таких как микроконтроллеры и мобильные устройства.

Принцип же дистилляции заключается в том, что "большая" модель (teacher model) обучает "меньшую" модель (student model), передавая ей свои знания в форме предсказаний.

В процессе дистилляции модель-учитель генерирует вероятностные распределения классов, которые затем используются для обучения модели-ученика.

Эти распределения, также называемые "мягкими метками" (soft labels), содержат более полную информацию, чем жёсткие метки (hard labels), так как отражают уверенность модели-учителя в каждом классе.

Сразу приводим пример дистилляции с квантованием.

Пример процесса дистилляции в PyTorch может выглядеть следующим образом:

import torch
import torch.nn.functional as F
def distillation_loss(student_output, teacher_output, labels, T, alpha):
    soft_loss = F.kl_div(F.log_softmax(student_output / T, dim=1),
                         F.softmax(teacher_output / T, dim=1), reduction='batchmean') * (T * T)
    hard_loss = F.cross_entropy(student_output, labels)
    return soft_loss * alpha + hard_loss * (1. - alpha)
  for data, labels in train_loader:
    student_output = student_model(data)
    with torch.no_grad():
        teacher_output = teacher_model(data)
    loss = distillation_loss(student_output, teacher_output, labels, T=4.0, alpha=0.7)
    loss.backward()
    optimizer.step()


71dece063505cb5f8d594e3220106b06.png

Функция distillation_loss объединяет два компонента:

  1. soft loss, который вычисляется с использованием распределений предсказаний модели-учителя и модели-ученика, нормализованных через температуру.

Это помогает передать модели-ученику более детализированную информацию о вероятностях классов, а не только о правильном классе (жёсткие метки), что делает процесс обучения более информативным.

  1. hard loss — стандартная функция кросс-энтропии, которая измеряет расстояние между предсказаниями модели-ученика и реальными метками классов.

Комбинация этих двух составляющих (в зависимости от значения параметра α) позволяет модели-ученику лучше учиться на основе предсказаний модели-учителя.

Процесс обучения модели-ученика:
В этом коде цикл обучения модели-ученика выглядит следующим образом:

Для каждой порции данных (мини-батч) выполняется инференс как на модели-ученике, так и на модели-учителе.

Предсказания модели-учителя передаются в функцию потерь, где они используются для вычисления soft loss.

Функция потерь комбинирует это с традиционной кросс-энтропией (hard loss), обучая модель-ученика более эффективно.

Затем выполняется шаг оптимизации, и модель-ученик обновляет свои веса на основе полученной комбинированной функции потерь.

После обучения модели-ученика с использованием метода дистилляции, она может быть квантована с применением стандартных методов, таких как динамическое или статическое квантование, что ещё больше уменьшит её размеры и потребление ресурсов.

Интеграция всех трёх методов — квантования, pruning и distillation — представляет собой мощный подход к сжатию моделей.

В реальных сценариях, таких как мобильные устройства или встроенные системы, это позволяет достигать значительных улучшений в скорости выполнения модели и её энергоэффективности.

Например, если модель сначала подвергается прореживанию для удаления малозначимых связей, затем проходит процесс дистилляции для создания облегчённой версии, и, наконец, подвергается квантованию, можно достичь значительного уменьшения вычислительных затрат, не теряя при этом критически важной точности.

Это был краткий гайд по квантованию. Надеемся, для некоторых, особенно новичков, он был полезен.

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  • 07.09.23 16:24 CherryTeam

    Cherry Team atlyginimų skaičiavimo programa yra labai naudingas įrankis įmonėms, kai reikia efektyviai valdyti ir skaičiuoti darbuotojų atlyginimus. Ši programinė įranga, turinti išsamias funkcijas ir patogią naudotojo sąsają, suteikia daug privalumų, kurie padeda supaprastinti darbo užmokesčio skaičiavimo procesus ir pagerinti finansų valdymą. Štai keletas pagrindinių priežasčių, kodėl Cherry Team atlyginimų skaičiavimo programa yra naudinga įmonėms: Automatizuoti ir tikslūs skaičiavimai: Atlyginimų skaičiavimai rankiniu būdu gali būti klaidingi ir reikalauti daug laiko. Programinė įranga Cherry Team automatizuoja visą atlyginimų skaičiavimo procesą, todėl nebereikia atlikti skaičiavimų rankiniu būdu ir sumažėja klaidų rizika. Tiksliai apskaičiuodama atlyginimus, įskaitant tokius veiksnius, kaip pagrindinis atlyginimas, viršvalandžiai, premijos, išskaitos ir mokesčiai, programa užtikrina tikslius ir be klaidų darbo užmokesčio skaičiavimo rezultatus. Sutaupoma laiko ir išlaidų: Darbo užmokesčio valdymas gali būti daug darbo jėgos reikalaujanti užduotis, reikalaujanti daug laiko ir išteklių. Programa Cherry Team supaprastina ir pagreitina darbo užmokesčio skaičiavimo procesą, nes automatizuoja skaičiavimus, generuoja darbo užmokesčio žiniaraščius ir tvarko išskaičiuojamus mokesčius. Šis automatizavimas padeda įmonėms sutaupyti daug laiko ir pastangų, todėl žmogiškųjų išteklių ir finansų komandos gali sutelkti dėmesį į strategiškai svarbesnę veiklą. Be to, racionalizuodamos darbo užmokesčio operacijas, įmonės gali sumažinti administracines išlaidas, susijusias su rankiniu darbo užmokesčio tvarkymu. Mokesčių ir darbo teisės aktų laikymasis: Įmonėms labai svarbu laikytis mokesčių ir darbo teisės aktų, kad išvengtų baudų ir teisinių problemų. Programinė įranga Cherry Team seka besikeičiančius mokesčių įstatymus ir darbo reglamentus, užtikrindama tikslius skaičiavimus ir teisinių reikalavimų laikymąsi. Programa gali dirbti su sudėtingais mokesčių scenarijais, pavyzdžiui, keliomis mokesčių grupėmis ir įvairių rūšių atskaitymais, todėl užtikrina atitiktį reikalavimams ir kartu sumažina klaidų riziką. Ataskaitų rengimas ir analizė: Programa Cherry Team siūlo patikimas ataskaitų teikimo ir analizės galimybes, suteikiančias įmonėms vertingų įžvalgų apie darbo užmokesčio duomenis. Ji gali generuoti ataskaitas apie įvairius aspektus, pavyzdžiui, darbo užmokesčio paskirstymą, išskaičiuojamus mokesčius ir darbo sąnaudas. Šios ataskaitos leidžia įmonėms analizuoti darbo užmokesčio tendencijas, nustatyti tobulintinas sritis ir priimti pagrįstus finansinius sprendimus. Pasinaudodamos duomenimis pagrįstomis įžvalgomis, įmonės gali optimizuoti savo darbo užmokesčio strategijas ir veiksmingai kontroliuoti išlaidas. Integracija su kitomis sistemomis: Cherry Team programinė įranga dažnai sklandžiai integruojama su kitomis personalo ir apskaitos sistemomis. Tokia integracija leidžia automatiškai perkelti atitinkamus duomenis, pavyzdžiui, informaciją apie darbuotojus ir finansinius įrašus, todėl nebereikia dubliuoti duomenų. Supaprastintas duomenų srautas tarp sistemų padidina bendrą efektyvumą ir sumažina duomenų klaidų ar neatitikimų riziką. Cherry Team atlyginimų apskaičiavimo programa įmonėms teikia didelę naudą - automatiniai ir tikslūs skaičiavimai, laiko ir sąnaudų taupymas, atitiktis mokesčių ir darbo teisės aktų reikalavimams, ataskaitų teikimo ir analizės galimybės bei integracija su kitomis sistemomis. Naudodamos šią programinę įrangą įmonės gali supaprastinti darbo užmokesčio skaičiavimo procesus, užtikrinti tikslumą ir atitiktį reikalavimams, padidinti darbuotojų pasitenkinimą ir gauti vertingų įžvalgų apie savo finansinius duomenis. Programa Cherry Team pasirodo esanti nepakeičiamas įrankis įmonėms, siekiančioms efektyviai ir veiksmingai valdyti darbo užmokestį. https://cherryteam.lt/lt/

  • 08.10.23 01:30 davec8080

    The "Shibarium for this confirmed rug pull is a BEP-20 project not related at all to Shibarium, SHIB, BONE or LEASH. The Plot Thickens. Someone posted the actual transactions!!!! https://bscscan.com/tx/0xa846ea0367c89c3f0bbfcc221cceea4c90d8f56ead2eb479d4cee41c75e02c97 It seems the article is true!!!! And it's also FUD. Let me explain. Check this link: https://bscscan.com/token/0x5a752c9fe3520522ea88f37a41c3ddd97c022c2f So there really is a "Shibarium" token. And somebody did a rug pull with it. CONFIRMED. But the "Shibarium" token for this confirmed rug pull is a BEP-20 project not related at all to Shibarium, SHIB, BONE or LEASH.

  • 24.06.24 04:31 tashandiarisha

    Web-site. https://trustgeekshackexpert.com/ Tele-Gram, trustgeekshackexpert During the pandemic, I ventured into the world of cryptocurrency trading. My father loaned me $10,000, which I used to purchase my first bitcoins. With diligent research and some luck, I managed to grow my investment to over $350,000 in just a couple of years. I was thrilled with my success, but my excitement was short-lived when I decided to switch brokers and inadvertently fell victim to a phishing attack. While creating a new account, I received what seemed like a legitimate email requesting verification. Without second-guessing, I provided my information, only to realize later that I had lost access to my email and cryptocurrency wallets. Panic set in as I watched my hard-earned assets disappear before my eyes. Desperate to recover my funds, I scoured the internet for solutions. That's when I stumbled upon the Trust Geeks Hack Expert on the Internet. The service claimed to specialize in recovering lost crypto assets, and I decided to take a chance. Upon contacting them, the team swung into action immediately. They guided me through the entire recovery process with professionalism and efficiency. The advantages of using the Trust Geeks Hack Expert Tool became apparent from the start. Their team was knowledgeable and empathetic, understanding the urgency and stress of my situation. They employed advanced security measures to ensure my information was handled safely and securely. One of the key benefits of the Trust Geeks Hack Expert Tool was its user-friendly interface, which made a complex process much more manageable for someone like me, who isn't particularly tech-savvy. They also offered 24/7 support, so I never felt alone during recovery. Their transparent communication and regular updates kept me informed and reassured throughout. The Trust Geeks Hack Expert Tool is the best solution for anyone facing similar issues. Their swift response, expertise, and customer-centric approach set them apart from other recovery services. Thanks to their efforts, I regained access to my accounts and my substantial crypto assets. The experience taught me a valuable lesson about online security and showed me the incredible potential of the Trust Geeks Hack Expert Tool. Email:: trustgeekshackexpert{@}fastservice{.}com WhatsApp  + 1.7.1.9.4.9.2.2.6.9.3

  • 26.06.24 18:46 Jacobethannn098

    LEGAL RECOUP FOR CRYPTO THEFT BY ADRIAN LAMO HACKER

  • 26.06.24 18:46 Jacobethannn098

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  • 04.07.24 04:49 ZionNaomi

    For over twenty years, I've dedicated myself to the dynamic world of marketing, constantly seeking innovative strategies to elevate brand visibility in an ever-evolving landscape. So when the meteoric rise of Bitcoin captured my attention as a potential avenue for investment diversification, I seized the opportunity, allocating $20,000 to the digital currency. Witnessing my investment burgeon to an impressive $70,000 over time instilled in me a sense of financial promise and stability.However, amidst the euphoria of financial growth, a sudden and unforeseen oversight brought me crashing back to reality during a critical business trip—I had misplaced my hardware wallet. The realization that I had lost access to the cornerstone of my financial security struck me with profound dismay. Desperate for a solution, I turned to the expertise of Daniel Meuli Web Recovery.Their response was swift . With meticulous precision, they embarked on the intricate process of retracing the elusive path of my lost funds. Through their unwavering dedication, they managed to recover a substantial portion of my investment, offering a glimmer of hope amidst the shadows of uncertainty. The support provided by Daniel Meuli Web Recovery extended beyond mere financial restitution. Recognizing the imperative of fortifying against future vulnerabilities, they generously shared invaluable insights on securing digital assets. Their guidance encompassed crucial aspects such as implementing hardware wallet backups and fortifying security protocols, equipping me with recovered funds and newfound knowledge to navigate the digital landscape securely.In retrospect, this experience served as a poignant reminder of the critical importance of diligence and preparedness in safeguarding one's assets. Thanks to the expertise and unwavering support extended by Daniel Meuli Web Recovery, I emerged from the ordeal with renewed resilience and vigilance. Empowered by their guidance and fortified by enhanced security measures, I now approach the future with unwavering confidence.The heights of financial promise to the depths of loss and back again has been a humbling one, underscoring the volatility and unpredictability inherent in the digital realm. Yet, through adversity, I have emerged stronger, armed with a newfound appreciation for the importance of diligence, preparedness, and the invaluable support of experts like Daniel Meuli Web Recovery.As I persist in traversing the digital landscape, I do so with a judicious blend of vigilance and fortitude, cognizant that with adequate safeguards and the backing of reliable confidants, I possess the fortitude to withstand any adversity that may arise. For this, I remain eternally appreciative. Email Danielmeuliweberecovery @ email . c om WhatsApp + 393 512 013 528

  • 13.07.24 21:13 michaelharrell825

    In 2020, amidst the economic fallout of the pandemic, I found myself unexpectedly unemployed and turned to Forex trading in hopes of stabilizing my finances. Like many, I was drawn in by the promise of quick returns offered by various Forex robots, signals, and trading advisers. However, most of these products turned out to be disappointing, with claims that were far from reality. Looking back, I realize I should have been more cautious, but the allure of financial security clouded my judgment during those uncertain times. Amidst these disappointments, Profit Forex emerged as a standout. Not only did they provide reliable service, but they also delivered tangible results—a rarity in an industry often plagued by exaggerated claims. The positive reviews from other users validated my own experience, highlighting their commitment to delivering genuine outcomes and emphasizing sound financial practices. My journey with Profit Forex led to a net profit of $11,500, a significant achievement given the challenges I faced. However, my optimism was short-lived when I encountered obstacles trying to withdraw funds from my trading account. Despite repeated attempts, I found myself unable to access my money, leaving me frustrated and uncertain about my financial future. Fortunately, my fortunes changed when I discovered PRO WIZARD GIlBERT RECOVERY. Their reputation for recovering funds from fraudulent schemes gave me hope in reclaiming what was rightfully mine. With a mixture of desperation and cautious optimism, I reached out to them for assistance. PRO WIZARD GIlBERT RECOVERY impressed me from the start with their professionalism and deep understanding of financial disputes. They took a methodical approach, using advanced techniques to track down the scammers responsible for withholding my funds. Throughout the process, their communication was clear and reassuring, providing much-needed support during a stressful period. Thanks to PRO WIZARD GIlBERT RECOVERY's expertise and unwavering dedication, I finally achieved a resolution to my ordeal. They successfully traced and retrieved my funds, restoring a sense of justice and relief. Their intervention not only recovered my money but also renewed my faith in ethical financial services. Reflecting on my experience, I've learned invaluable lessons about the importance of due diligence and discernment in navigating the Forex market. While setbacks are inevitable, partnering with reputable recovery specialists like PRO WIZARD GIlBERT RECOVERY can make a profound difference. Their integrity and effectiveness have left an indelible mark on me, guiding my future decisions and reinforcing the value of trustworthy partnerships in achieving financial goals. I wholeheartedly recommend PRO WIZARD GIlBERT RECOVERY to anyone grappling with financial fraud or disputes. Their expertise and commitment to client satisfaction are unparalleled, offering a beacon of hope in challenging times. Thank you, PRO WIZARD GIlBERT RECOVERY, for your invaluable assistance in reclaiming what was rightfully mine. Your service not only recovered my funds but also restored my confidence in navigating the complexities of financial markets with greater caution and awareness. Email: prowizardgilbertrecovery(@)engineer.com Homepage: https://prowizardgilbertrecovery.xyz WhatsApp: +1 (516) 347‑9592

  • 17.07.24 02:26 thompsonrickey

    In the vast and often treacherous realm of online investments, I was entangled in a web of deceit that cost me nearly  $45,000. It all started innocuously enough with an enticing Instagram profile promising lucrative returns through cryptocurrency investment. Initially, everything seemed promising—communications were smooth, and assurances were plentiful. However, as time passed, my optimism turned to suspicion. Withdrawal requests were met with delays and excuses. The once-responsive "investor" vanished into thin air, leaving me stranded with dwindling hopes and a sinking feeling in my gut. It became painfully clear that I had been duped by a sophisticated scheme designed to exploit trust and naivety. Desperate to recover my funds, I turned to online forums where I discovered numerous testimonials advocating for Muyern Trust Hacker. With nothing to lose, I contacted them, recounting my ordeal with a mixture of skepticism and hope. Their swift response and professional demeanor immediately reassured me that I had found a lifeline amidst the chaos. Muyern Trust Hacker wasted no time in taking action. They meticulously gathered evidence, navigated legal complexities, and deployed their expertise to expedite recovery. In what felt like a whirlwind of activity, although the passage of time was a blur amidst my anxiety, they achieved the seemingly impossible—my stolen funds were returned. The relief I felt was overwhelming. Muyern Trust Hacker not only restored my financial losses but also restored my faith in justice. Their commitment to integrity and their relentless pursuit of resolution were nothing short of remarkable. They proved themselves as recovery specialists and guardians against digital fraud, offering hope to victims like me who had been ensnared by deception. My gratitude knows no bounds for Muyern Trust Hacker. Reach them at muyerntrusted @ m a i l - m e . c o m AND Tele gram @ muyerntrusthackertech

  • 18.07.24 20:13 austinagastya

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  • 27.08.24 12:50 James889900

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  • 27.08.24 13:06 James889900

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  • 02.09.24 20:24 [email protected]

    If You Need Hacker To Recover Your Bitcoin Contact Paradox Recovery Wizard Paradox Recovery Wizard successfully recovered $123,000 worth of Bitcoin for my husband, which he had lost due to a security breach. The process was efficient and secure, with their expert team guiding us through each step. They were able to trace and retrieve the lost cryptocurrency, restoring our peace of mind and financial stability. Their professionalism and expertise were instrumental in recovering our assets, and we are incredibly grateful for their service. Email: support@ paradoxrecoverywizard.com Email: paradox_recovery @cyberservices.com Wep: https://paradoxrecoverywizard.com/ WhatsApp: +39 351 222 3051.

  • 06.09.24 01:35 Celinagarcia

    HOW TO RECOVER MONEY LOST IN BITCOIN/USDT TRADING OR TO CRYPTO INVESTMENT !! Hi all, friends and families. I am writing From Alberton Canada. Last year I tried to invest in cryptocurrency trading in 2023, but lost a significant amount of money to scammers. I was cheated of my money, but thank God, I was referred to Hack Recovery Wizard they are among the best bitcoin recovery specialists on the planet. they helped me get every penny I lost to the scammers back to me with their forensic techniques. and I would like to take this opportunity to advise everyone to avoid making cryptocurrency investments online. If you ​​​​​​have already lost money on forex, cryptocurrency or Ponzi schemes, please contact [email protected] or WhatsApp: +1 (757) 237–1724 at once they can help you get back the crypto you lost to scammers. BEST WISHES. Celina Garcia.

  • 06.09.24 01:44 Celinagarcia

    HOW TO RECOVER MONEY LOST IN BITCOIN/USDT TRADING OR TO CRYPTO INVESTMENT !! Hi all, friends and families. I am writing From Alberton Canada. Last year I tried to invest in cryptocurrency trading in 2023, but lost a significant amount of money to scammers. I was cheated of my money, but thank God, I was referred to Hack Recovery Wizard they are among the best bitcoin recovery specialists on the planet. they helped me get every penny I lost to the scammers back to me with their forensic techniques. and I would like to take this opportunity to advise everyone to avoid making cryptocurrency investments online. If you ​​​​​​have already lost money on forex, cryptocurrency or Ponzi schemes, please contact [email protected] or WhatsApp: +1 (757) 237–1724 at once they can help you get back the crypto you lost to scammers. BEST WISHES. Celina Garcia.

  • 16.09.24 00:10 marcusaustin

    Bitcoin Recovery Services: Restoring Lost Cryptocurrency If you've lost access to your cryptocurrency and unable to make a withdrawal, I highly recommend iBolt Cyber Hacker Bitcoin Recovery Services. Their team is skilled, professional, and efficient in recovering lost Bitcoin. They provide clear communication, maintain high security standards, and work quickly to resolve issues. Facing the stress of lost cryptocurrency, iBolt Cyber Hacker is a trusted service that will help you regain access to your funds securely and reliably. Highly recommended! Email: S u p p o r t @ ibolt cyber hack . com Cont/Whtp + 3. .9 .3. .5..0. .9. 2. 9. .0 .3. 1 .8. Website: h t t p s : / / ibolt cyber hack . com /

  • 16.09.24 00:11 marcusaustin

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  • 23.09.24 18:56 matthewshimself

    At first, I was admittedly skeptical about Worldcoin (ref: https://worldcoin.org/blog/worldcoin/this-is-worldcoin-video-explainer-series), particularly around the use of biometric data and the WLD token as a reward mechanism for it. However, after following the project closer, I’ve come to appreciate the broader vision and see the value in the underlying tech behind it. The concept of Proof of Personhood (ref: https://worldcoin.org/blog/worldcoin/proof-of-personhood-what-it-is-why-its-needed) has definitely caught my attention, and does seem like a crucial step towards tackling growing issues like bots, deepfakes, and identity fraud. Sam Altman’s vision is nothing short of ambitious, but I do think he & Alex Blania have the chops to realize it as mainstay in the global economy.

  • 01.10.24 14:54 Sinewclaudia

    I lost about $876k few months ago trading on a fake binary option investment websites. I didn't knew they were fake until I tried to withdraw. Immediately, I realized these guys were fake. I contacted Sinew Claudia world recovery, my friend who has such experience before and was able to recover them, recommended me to contact them. I'm a living testimony of a successful recovery now. You can contact the legitimate recovery company below for help and assistance. [email protected] [email protected] WhatsApp: 6262645164

  • 02.10.24 22:27 Emily Hunter

    Can those who have fallen victim to fraud get their money back? Yes, you might be able to get back what was taken from you if you fell prey to a fraud from an unregulated investing platform or any other scam, but only if you report it to the relevant authorities. With the right plan and supporting documentation, you can get back what you've lost. Most likely, the individuals in control of these unregulated platforms would attempt to convince you that what happened to your money was a sad accident when, in fact, it was a highly skilled heist. You should be aware that there are resources out there to help you if you or someone you know has experienced one of these circumstances. Do a search using (deftrecoup (.) c o m). Do not let the perpetrators of this hoaxes get away with ruining you mentally and financially.

  • 18.10.24 09:34 freidatollerud

    The growth of WIN44 in Brazil is very interesting! If you're looking for more options for online betting and casino games, I recommend checking out Casinos in Brazil. It's a reliable platform that offers a wide variety of games and provides a safe and enjoyable experience for users. It's worth checking out! https://win44.vip

  • 31.10.24 00:13 ytre89

    Can those who have fallen victim to fraud get their money back? Yes, you might be able to get back what was taken from you if you fell prey to a fraud from an unregulated investing platform or any other scam, but only if you report it to the relevant authorities. With the right plan and supporting documentation, you can get back what you've lost. Most likely, the individuals in control of these unregulated platforms would attempt to convince you that what happened to your money was a sad accident when, in fact, it was a highly skilled heist. You should be aware that there are resources out there to help you if you or someone you know has experienced one of these circumstances. Do a search using (deftrecoup (.) c o m). Do not let the perpetrators of this hoaxes get away with ruining you mentally and financially.

  • 02.11.24 14:44 diannamendoza732

    In the world of Bitcoin recovery, Pro Wizard Gilbert truly represents the gold standard. My experience with Gilbert revealed just how exceptional his methods are and why he stands out as the premier authority in this critical field. When I first encountered the complexities of Bitcoin recovery, I was daunted by the technical challenges and potential risks. Gilbert’s approach immediately distinguished itself through its precision and effectiveness. His methods are meticulously designed, combining cutting-edge techniques with an in-depth understanding of the Bitcoin ecosystem. He tackled the recovery process with a level of expertise and thoroughness that was both impressive and reassuring. What sets Gilbert’s methods apart is not just their technical sophistication but also their strategic depth. He conducts a comprehensive analysis of each case, tailoring his approach to address the unique aspects of the situation. This personalized strategy ensures that every recovery effort is optimized for success. Gilbert’s transparent communication throughout the process was invaluable, providing clarity and confidence during each stage of the recovery. The results I achieved with Pro Wizard Gilbert’s methods were remarkable. His gold standard approach not only recovered my Bitcoin but did so with an efficiency and reliability that exceeded my expectations. His deep knowledge, innovative techniques, and unwavering commitment make him the definitive expert in Bitcoin recovery. For anyone seeking a benchmark in Bitcoin recovery solutions, Pro Wizard Gilbert’s methods are the epitome of excellence. His ability to blend technical prowess with strategic insight truly sets him apart in the industry. Call: for help. You may get in touch with them at ; Email: (prowizardgilbertrecovery(@)engineer.com) Telegram ; https://t.me/Pro_Wizard_Gilbert_Recovery Homepage ; https://prowizardgilbertrecovery.info

  • 12.11.24 00:50 TERESA

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  • 17.11.24 09:31 Vivianlocke223

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  • 19.11.24 03:06 [email protected]

    My entire existence fell apart when a malevolent hacker recently gained access to my online accounts. I felt violated and extremely uneasy after discovering that the digital platforms I depended on for communication, employment, and finances had been compromised. Regaining control and restoring my digital security was an overwhelming task in the immediate aftermath. To help me navigate the difficult process of recovering my accounts and getting my peace of mind back, TRUST GEEKS HACK EXPERT came into my life as a ray of hope. They immediately put their highly skilled professionals to work, thoroughly examining the vulnerability and methodically preventing unwanted access. They guided me through each stage soothingly, explaining what was occurring and why, so I never felt lost or alone. They communicated with service providers to restore my legitimate access while skillfully navigating the complex labyrinth of account recovery procedures. My digital footprint was cleaned and strengthened against future attacks thanks to their equally amazing ability to remove any remaining evidence of the hacker's presence. However, TRUST GEEKS HACK EXPERT actual worth went beyond its technical aspects. They offered constant emotional support during the ordeal, understanding my fragility and sense of violation. My tense nerves were calmed by their comforting presence and kind comments, which served as a reminder that I wasn't alone in this struggle. With their help, I was able to reestablish my sense of security and control, which enabled me to return my attention to the significant areas of my life that had been upended. Ultimately, TRUST GEEKS HACK EXPERT all-encompassing strategy not only recovered my online accounts but also my general peace of mind, which is a priceless result for which I am incredibly appreciative of their knowledge and kindness. Make the approach and send a message to TRUST GEEKS HACK EXPERT Via Web site <> www://trustgeekshackexpert.com/-- E>mail: Trustgeekshackexpert(At)fastservice..com -- TeleGram,<> Trustgeekshackexpert

  • 19.11.24 03:07 [email protected]

    My entire existence fell apart when a malevolent hacker recently gained access to my online accounts. I felt violated and extremely uneasy after discovering that the digital platforms I depended on for communication, employment, and finances had been compromised. Regaining control and restoring my digital security was an overwhelming task in the immediate aftermath. To help me navigate the difficult process of recovering my accounts and getting my peace of mind back, TRUST GEEKS HACK EXPERT came into my life as a ray of hope. They immediately put their highly skilled professionals to work, thoroughly examining the vulnerability and methodically preventing unwanted access. They guided me through each stage soothingly, explaining what was occurring and why, so I never felt lost or alone. They communicated with service providers to restore my legitimate access while skillfully navigating the complex labyrinth of account recovery procedures. My digital footprint was cleaned and strengthened against future attacks thanks to their equally amazing ability to remove any remaining evidence of the hacker's presence. However, TRUST GEEKS HACK EXPERT actual worth went beyond its technical aspects. They offered constant emotional support during the ordeal, understanding my fragility and sense of violation. My tense nerves were calmed by their comforting presence and kind comments, which served as a reminder that I wasn't alone in this struggle. With their help, I was able to reestablish my sense of security and control, which enabled me to return my attention to the significant areas of my life that had been upended. Ultimately, TRUST GEEKS HACK EXPERT all-encompassing strategy not only recovered my online accounts but also my general peace of mind, which is a priceless result for which I am incredibly appreciative of their knowledge and kindness. Make the approach and send a message to TRUST GEEKS HACK EXPERT Via Web site <> www://trustgeekshackexpert.com/-- E>mail: Trustgeekshackexpert(At)fastservice..com -- TeleGram,<> Trustgeekshackexpert

  • 21.11.24 04:14 ronaldandre617

    Being a parent is great until your toddler figures out how to use your devices. One afternoon, I left my phone unattended for just a few minutes rookie mistake of the century. I thought I’d take a quick break, but little did I know that my curious little genius was about to embark on a digital adventure. By the time I came back, I was greeted by two shocking revelations: my toddler had somehow managed to buy a $5 dinosaur toy online and, even more alarmingly, had locked me out of my cryptocurrency wallet holding a hefty $75,000. Yes, you heard that right a dinosaur toy was the least of my worries! At first, I laughed it off. I mean, what toddler doesn’t have a penchant for expensive toys? But then reality set in. I stared at my phone in disbelief, desperately trying to guess whatever random string of gibberish my toddler had typed as a new password. Was it “dinosaur”? Or perhaps “sippy cup”? I felt like I was in a bizarre game of Password Gone Wrong. Every attempt led to failure, and soon the laughter faded, replaced by sheer panic. I was in way over my head, and my heart raced as the countdown of time ticked away. That’s when I decided to take action and turned to Digital Tech Guard Recovery, hoping they could solve the mystery that was my toddler’s handiwork. I explained my predicament, half-expecting them to chuckle at my misfortune, but they were incredibly professional and empathetic. Their confidence put me at ease, and I knew I was in good hands. Contact With WhatsApp: +1 (443) 859 - 2886  Email digital tech guard . com  Telegram: digital tech guard recovery . com  website link :: https : // digital tech guard . com Their team took on the challenge like pros, employing their advanced techniques to unlock my wallet with a level of skill I can only describe as magical. As I paced around, anxiously waiting for updates, I imagined my toddler inadvertently locking away my life savings forever. But lo and behold, it didn’t take long for Digital Tech Guard Recovery to work their magic. Not only did they recover the $75,000, but they also gave me invaluable tips on securing my wallet better like not leaving it accessible to tiny fingers! Who knew parenting could lead to such dramatic situations? Crisis averted, and I learned my lesson: always keep my devices out of reach of little explorers. If you ever find yourself in a similar predicament whether it’s tech-savvy toddlers or other digital disasters don’t hesitate to reach out to Digital Tech Guard Recovery. They saved my funds and my sanity, proving that no challenge is too great, even when it involves a toddler’s mischievous fingers!

  • 21.11.24 08:02 Emily Hunter

    If I hadn't found a review online and filed a complaint via email to support@deftrecoup. com , the people behind this unregulated scheme would have gotten away with leaving me in financial ruins. It was truly the most difficult period of my life.

  • 22.11.24 04:41 [email protected]

    I never could have imagined the nightmare of losing access to my digital wallet. All of my cryptocurrency holdings were abruptly imprisoned, inaccessible, and appeared to be lost forever following a catastrophic hardware breakdown. Years of meticulous investment and careful saving were reduced to nothing more than strings of code that I could no longer control, and I could feel the dread and sorrow that swept through me at that very instant. Thankfully, during my worst moment, I came into (TRUST GEEKS HACK EXPERT), a professional service devoted to recovering lost or inaccessible digital data. With optimism, I went out to their team of skilled technologists, laying bare the full nature of my issue. What followed was a laborious, multi-step process that required an almost surgical level of digital forensics and Bitcoin skill. In order to create a thorough profile of my wallet's contents and activities, the (TRUST GEEKS HACK EXPERT) team first thoroughly examined the transaction history and metadata connected to it. Next, they implemented a series of advanced recovery techniques, using cutting-edge software tools to bypass the access barriers that had left me locked out. The entire process was shrouded in secrecy and discretion, with the (TRUST GEEKS HACK EXPERT) team working tirelessly to protect the confidentiality of my sensitive financial information. After what felt like an eternity of nervous anticipation, the day finally arrived when I received the triumphant notification – my wallet had been successfully restored, and all of my precious digital assets had been returned to my control. The sense of relief was indescribable, as I could finally breathe easy knowing that the fruits of my financial discipline had been safeguarded. While the experience of losing access to my wallet was undoubtedly traumatic, (TRUST GEEKS HACK EXPERT) intervention allowed me to emerge from the ordeal with my cryptocurrency holdings intact, and a renewed appreciation for the importance of proactive digital asset management. You can contact Them through EMAIL: [email protected] - TELEGRAM: TRUSTGEEKSHACKEXPERT

  • 22.11.24 15:26 cliftonhandyman

    Your Lost Bitcoins Are Not Gone Forever? Enquire From iBolt Cyber Hacker iBolt Cyber Hacker is a cybersecurity service that specializes in Bitcoin and cryptocurrency recovery. Even if your Bitcoin is locked away in a scammer inaccessible wallet, they have the tools and expertise to retrieve it. Many people, including seasoned cryptocurrency investors, face the daunting possibility of never seeing their lost funds again. iBolt cyber hacker service is a potential lifeline in these situations. I understand the concerns many people might have about trusting a third-party service to recover their Bitcoin. iBolt Cyber Hacker takes security seriously, implementing encryption and stringent privacy protocols. I was assured that no sensitive data would be compromised during the recovery process. Furthermore, their reputation in the cryptocurrency community, based on positive feedback from previous clients, gave me confidence that I was in good hands. Whtp +39, 351..105, 3619 Em.ail: ibolt @ cyber- wizard. co m

  • 22.11.24 23:43 teresaborja

    all thanks to Tech Cyber Force Recovery expert assistance. As a novice in cryptocurrency, I had been carefully accumulating a modest amount of Bitcoin, meticulously safeguarding my digital wallet and private keys. However, as the adage goes, the best-laid plans can often go awry, and that's precisely what happened to me. Due to a series of technical mishaps and human errors, I found myself locked out of my Bitcoin wallet, unable to access the fruits of my digital labors. Panic set in as I frantically searched for a solution, scouring the internet for any glimmer of hope. That's when I stumbled upon the Tech Cyber Force Recovery team, a group of seasoned cryptocurrency specialists who had built a reputation for their ability to recover lost or inaccessible digital assets. Skeptical at first, I reached out, desperate for a miracle. To my utter amazement, the Tech Cyber Force Recovery experts quickly assessed my situation and devised a meticulous plan of attack. Through their deep technical knowledge, unwavering determination, and a keen eye for detail, they were able to navigate the complex labyrinth of blockchain technology, ultimately recovering my entire Bitcoin portfolio. What had once seemed like a hopeless endeavor was now a reality, and I found myself once again in possession of my digital wealth, all thanks to the incredible efforts of the Tech Cyber Force Recovery team. This experience has not only restored my faith in the cryptocurrency ecosystem. Still, it has also instilled in me a profound appreciation for the critical role that expert recovery services can play in safeguarding one's digital assets.   ENAIL < Tech cybers force recovery @ cyber services. com >   WEBSITE < ht tps : // tech cyber force recovery. info  >   TEXT < +1. 561. 726. 3697 >

  • 24.11.24 02:21 [email protected]

    I never could have imagined the nightmare of losing access to my digital wallet. All of my cryptocurrency holdings were abruptly imprisoned, inaccessible, and appeared to be lost forever following a catastrophic hardware breakdown. Years of meticulous investment and careful saving were reduced to nothing more than strings of code that I could no longer control, and I could feel the dread and sorrow that swept through me at that very instant. Thankfully, during my worst moment, I came into (TRUST GEEKS HACK EXPERT), a professional service devoted to recovering lost or inaccessible digital data. With optimism, I went out to their team of skilled technologists, laying bare the full nature of my issue. What followed was a laborious, multi-step process that required an almost surgical level of digital forensics and Bitcoin skill. In order to create a thorough profile of my wallet's contents and activities, the (TRUST GEEKS HACK EXPERT) team first thoroughly examined the transaction history and metadata connected to it. Next, they implemented a series of advanced recovery techniques, using cutting-edge software tools to bypass the access barriers that had left me locked out. The entire process was shrouded in secrecy and discretion, with the (TRUST GEEKS HACK EXPERT) team working tirelessly to protect the confidentiality of my sensitive financial information. After what felt like an eternity of nervous anticipation, the day finally arrived when I received the triumphant notification – my wallet had been successfully restored, and all of my precious digital assets had been returned to my control. The sense of relief was indescribable, as I could finally breathe easy knowing that the fruits of my financial discipline had been safeguarded. While the experience of losing access to my wallet was undoubtedly traumatic, (TRUST GEEKS HACK EXPERT) intervention allowed me to emerge from the ordeal with my cryptocurrency holdings intact, and a renewed appreciation for the importance of proactive digital asset management. You can contact Them through EMAIL: [email protected] - TELEGRAM: TRUSTGEEKSHACKEXPERT

  • 02:19 briankennedy

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  • 02:20 briankennedy

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