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#include <memory>
#include <deque>
#include <cmath>
#include <cstring>
/*
the algorithm used here is taken and modified from:
https://stackoverflow.com/questions/9625663/calculating-and-printing-the-nth-prime-number/9704912#9704912
There are many more room of possible imprevement.
// erick[dot]wahyutama[at]gmail.com
// Ery E. Wahyutama
#include <unordered_map>
// https://github.com/json-c/json-c
#include <json-c/json.h>
#ifndef byte
typedef unsigned char byte;
#endif