#include <bits/stdc++.h>
int n, q;
int a[300000];
int go[300000][19] = {0};
int last[300000][19] = {0};
void Init() {
  scanf("%d%d", &n, &q);
  int last_index[19] = {0};
  int max_bits;
  for (int i = 0; i < n; i++) {
    scanf("%d", a + i);
    int bit = 0;
    while ((1 << bit) <= a[i]) {
      if (a[i] & (1 << bit)) {
        for (int j = last_index[bit]; j < i; j++) {
          last[j][bit] = i + 1;
        }
        last_index[bit] = i;
      }
      bit++;
    }
    max_bits = std::max(max_bits, bit);
  }
  for (int i = n - 1; i >= 0; i--) {
    for (int bit = 0; bit < max_bits; bit++) {
      if (a[i] & (1 << bit)) {
        go[i][bit] = i + 1;
      } else {
        int minJump = 0;
        int b = 0;
        while ((1 << b) <= a[i]) {
          if (a[i] & (1 << b)) {
            int jump_last = last[i][b];
            if (jump_last > 0 && go[jump_last - 1][bit] > 0) {
              int jump_go = go[jump_last - 1][bit];
              minJump = !minJump ? jump_go : std::min(minJump, jump_go);
            }
          }
          b++;
        }
        if (bit >= 19) {
          std::cout << max_bits << std::endl;
        }
        go[i][bit] = minJump;
      }
    }
  }
}
int main(int argc, char const *argv[]) {
  Init();
  for (int i = 0; i < q; i++) {
    int x, y;
    scanf("%d%d", &x, &y);
    int ax = a[x - 1], ay = a[y - 1];
    bool ans = false;
    int bit = 0;
    while ((1 << bit) <= ay) {
      if (ay & (1 << bit) && go[x - 1][bit] > 0 && go[x - 1][bit] <= y) {
        ans = true;
        break;
      }
      bit++;
    }
    if (ans) {
      printf("Shi\n");
    } else {
      printf("Fou\n");
    }
  }
  return 0;
}

### Prompt

In cpp, your task is to solve the following problem:

Toad Pimple has an array of integers a_1, a_2, …, a_n.

We say that y is reachable from x if x<y and there exists an integer array p such that x = p_1 < p_2 < … < p_k=y, and a_{p_i}  \&  a_{p_{i+1}} > 0 for all integers i such that 1 ≤ i < k.

Here \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).

You are given q pairs of indices, check reachability for each of them.

Input

The first line contains two integers n and q (2 ≤ n ≤ 300 000, 1 ≤ q ≤ 300 000) — the number of integers in the array and the number of queries you need to answer.

The second line contains n space-separated integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 300 000) — the given array.

The next q lines contain two integers each. The i-th of them contains two space-separated integers x_i and y_i (1 ≤ x_i < y_i ≤ n). You need to check if y_i is reachable from x_i. 

Output

Output q lines. In the i-th of them print "Shi" if y_i is reachable from x_i, otherwise, print "Fou".

Example

Input


5 3
1 3 0 2 1
1 3
2 4
1 4


Output


Fou
Shi
Shi

Note

In the first example, a_3 = 0. You can't reach it, because AND with it is always zero. a_2  \&  a_4 > 0, so 4 is reachable from 2, and to go from 1 to 4 you can use p = [1, 2, 4].

### Response

```cpp
#include <bits/stdc++.h>
int n, q;
int a[300000];
int go[300000][19] = {0};
int last[300000][19] = {0};
void Init() {
  scanf("%d%d", &n, &q);
  int last_index[19] = {0};
  int max_bits;
  for (int i = 0; i < n; i++) {
    scanf("%d", a + i);
    int bit = 0;
    while ((1 << bit) <= a[i]) {
      if (a[i] & (1 << bit)) {
        for (int j = last_index[bit]; j < i; j++) {
          last[j][bit] = i + 1;
        }
        last_index[bit] = i;
      }
      bit++;
    }
    max_bits = std::max(max_bits, bit);
  }
  for (int i = n - 1; i >= 0; i--) {
    for (int bit = 0; bit < max_bits; bit++) {
      if (a[i] & (1 << bit)) {
        go[i][bit] = i + 1;
      } else {
        int minJump = 0;
        int b = 0;
        while ((1 << b) <= a[i]) {
          if (a[i] & (1 << b)) {
            int jump_last = last[i][b];
            if (jump_last > 0 && go[jump_last - 1][bit] > 0) {
              int jump_go = go[jump_last - 1][bit];
              minJump = !minJump ? jump_go : std::min(minJump, jump_go);
            }
          }
          b++;
        }
        if (bit >= 19) {
          std::cout << max_bits << std::endl;
        }
        go[i][bit] = minJump;
      }
    }
  }
}
int main(int argc, char const *argv[]) {
  Init();
  for (int i = 0; i < q; i++) {
    int x, y;
    scanf("%d%d", &x, &y);
    int ax = a[x - 1], ay = a[y - 1];
    bool ans = false;
    int bit = 0;
    while ((1 << bit) <= ay) {
      if (ay & (1 << bit) && go[x - 1][bit] > 0 && go[x - 1][bit] <= y) {
        ans = true;
        break;
      }
      bit++;
    }
    if (ans) {
      printf("Shi\n");
    } else {
      printf("Fou\n");
    }
  }
  return 0;
}

```