fast I:O.cpp

// fast in version 1

template <class T>
void fastInput(T &N) {
    char ch;
    int sign = 1;
    N = 0;
    while ((ch = getchar_unlocked()) && ch == ' ') {};
    if (ch == '-') sign = -1;
    else if (isdigit(ch)) N = ch - '0';
    while ((ch = getchar_unlocked()) && isdigit(ch)) {
        N = (N << 1) + (N << 3) + ch - '0';
    }
    if (sign == -1) N = ~N + 1;
}


// fast in version 2

template <class T> void fastInput(T &n){
    char ch;
    int sign = 1;
    while(ch = getchar_unlocked(), isspace(ch)) {
        
    };
    n = 0;
    if(ch == '-')
        sign = -1;
    else n = ch - '0';
    while(ch = getchar_unlocked(), isdigit(ch))
        n = (n << 3) + (n << 1) + ch - '0';
    n *= sign;
}


// fast out

template<class T> void fastPrint(T n){
    if(n == 0){
        puts("0");
        return;
    }
    char buffer[256];
    int ptr = 0, sign = 1;
    
    if(n < 0){
        sign = -1;
        n *= -1;
    }
    while(n > 0){
        buffer[ptr ++] = (char)(n % 10 + '0');
        n /= 10;
    }
    if(sign == -1)
        putchar_unlocked('-');
    for(int i = ptr - 1; i >= 0; i --)
        putchar_unlocked(buffer[i]);
    putchar_unlocked('\n');
}