fastIO

void read(int& x) {
  int neg = 0; x = 0;
  char t = getchar();
  while ((t < 48 || t > 57) && t != '-') t = getchar();
  if (t == '-') { neg = 1; t = getchar(); }
  while (t >= 48 && t <= 57) {
    x = (x << 3) + (x << 1) + t - 48;
    t = getchar();
  }
  if (neg) x = -x;
}

void write(int x) {
  if (x == 0) { putchar('0'); return; }
  if (x < 0) { putchar('-'); x = -x; }
  char a[20]; a[0] = '0';
  int i = 0;
  while (x) {
    a[i++] = x % 10 + 48;
    x /= 10;
  }
  for (int j = i - 1; j >= 0; j--) putchar(a[j]);
}