#include <bits/stdc++.h>
using namespace std;
const int MAXN = 200005;
int n, q;
int arr[MAXN];
int ck[5] = {2, 0, 1, 7};
int seg[(1 << 19)][5][5];
int normal_ret[5][5];
struct data {
  int arr[5][5];
  data(int k[5][5]) {
    for (int i = 0; i < 5; i++) {
      for (int j = 0; j < 5; j++) {
        arr[i][j] = k[i][j];
      }
    }
  }
  data() {}
};
void build(int start, int end, int node) {
  if (start == end) {
    for (int i = 0; i <= 4; i++) {
      for (int j = i; j <= min(4, i + 1); j++) {
        if (i == j) {
          seg[node][i][i] = 0;
          if (i >= 3 && arr[start] == 6) seg[node][i][i] = 1;
          if (i != 4) {
            if (arr[start] == ck[i]) seg[node][i][i] = 1;
          }
        } else {
          if (arr[start] == ck[i])
            seg[node][i][j] = 0;
          else
            seg[node][i][j] = 1e9;
        }
      }
    }
    return;
  }
  build(start, (start + end) / 2, 2 * node);
  build((start + end) / 2 + 1, end, 2 * node + 1);
  for (int i = 0; i <= 4; i++) {
    for (int j = i; j <= 4; j++) {
      for (int k = i; k <= j; k++) {
        seg[node][i][j] =
            min(seg[node][i][j], seg[2 * node][i][k] + seg[2 * node + 1][k][j]);
      }
    }
  }
}
data query(int start, int end, int i, int j, int node) {
  if (start > j || end < i) {
    data x(normal_ret);
    return x;
  }
  if (start >= i && end <= j) {
    data x(seg[node]);
    return x;
  }
  data fi = query(start, (start + end) / 2, i, j, 2 * node);
  data si = query((start + end) / 2 + 1, end, i, j, 2 * node + 1);
  data ci;
  for (int i = 0; i < 5; i++) {
    for (int j = 0; j < 5; j++) ci.arr[i][j] = 1e9;
  }
  for (int i = 0; i <= 4; i++) {
    for (int j = i; j <= 4; j++) {
      for (int k = i; k <= j; k++) {
        ci.arr[i][j] = min(ci.arr[i][j], fi.arr[i][k] + si.arr[k][j]);
      }
    }
  }
  return ci;
}
int main() {
  for (int i = 0; i < (1 << 19); i++) {
    for (int j = 0; j < 5; j++) {
      for (int k = 0; k < 5; k++) {
        seg[i][j][k] = 1e9;
        normal_ret[j][k] = 1e9;
      }
    }
  }
  normal_ret[0][0] = normal_ret[4][4] = 0;
  ios_base::sync_with_stdio(0);
  cin >> n >> q;
  for (int i = 1; i <= n; i++) {
    char k;
    cin >> k;
    arr[i] = k - '0';
  }
  build(1, n, 1);
  for (int i = 0; i < q; i++) {
    int l, r;
    cin >> l >> r;
    data matrix = query(1, n, l, r, 1);
    if (matrix.arr[0][4] >= 1e8)
      cout << -1 << '\n';
    else
      cout << matrix.arr[0][4] << '\n';
  }
  return 0;
}

### Prompt

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

A string t is called nice if a string "2017" occurs in t as a subsequence but a string "2016" doesn't occur in t as a subsequence. For example, strings "203434107" and "9220617" are nice, while strings "20016", "1234" and "20167" aren't nice.

The ugliness of a string is the minimum possible number of characters to remove, in order to obtain a nice string. If it's impossible to make a string nice by removing characters, its ugliness is  - 1.

Limak has a string s of length n, with characters indexed 1 through n. He asks you q queries. In the i-th query you should compute and print the ugliness of a substring (continuous subsequence) of s starting at the index ai and ending at the index bi (inclusive).

Input

The first line of the input contains two integers n and q (4 ≤ n ≤ 200 000, 1 ≤ q ≤ 200 000) — the length of the string s and the number of queries respectively.

The second line contains a string s of length n. Every character is one of digits '0'–'9'.

The i-th of next q lines contains two integers ai and bi (1 ≤ ai ≤ bi ≤ n), describing a substring in the i-th query.

Output

For each query print the ugliness of the given substring.

Examples

Input

8 3
20166766
1 8
1 7
2 8


Output

4
3
-1


Input

15 5
012016662091670
3 4
1 14
4 15
1 13
10 15


Output

-1
2
1
-1
-1


Input

4 2
1234
2 4
1 2


Output

-1
-1

Note

In the first sample:

  * In the first query, ugliness("20166766") = 4 because all four sixes must be removed. 
  * In the second query, ugliness("2016676") = 3 because all three sixes must be removed. 
  * In the third query, ugliness("0166766") = - 1 because it's impossible to remove some digits to get a nice string. 



In the second sample:

  * In the second query, ugliness("01201666209167") = 2. It's optimal to remove the first digit '2' and the last digit '6', what gives a string "010166620917", which is nice. 
  * In the third query, ugliness("016662091670") = 1. It's optimal to remove the last digit '6', what gives a nice string "01666209170". 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 200005;
int n, q;
int arr[MAXN];
int ck[5] = {2, 0, 1, 7};
int seg[(1 << 19)][5][5];
int normal_ret[5][5];
struct data {
  int arr[5][5];
  data(int k[5][5]) {
    for (int i = 0; i < 5; i++) {
      for (int j = 0; j < 5; j++) {
        arr[i][j] = k[i][j];
      }
    }
  }
  data() {}
};
void build(int start, int end, int node) {
  if (start == end) {
    for (int i = 0; i <= 4; i++) {
      for (int j = i; j <= min(4, i + 1); j++) {
        if (i == j) {
          seg[node][i][i] = 0;
          if (i >= 3 && arr[start] == 6) seg[node][i][i] = 1;
          if (i != 4) {
            if (arr[start] == ck[i]) seg[node][i][i] = 1;
          }
        } else {
          if (arr[start] == ck[i])
            seg[node][i][j] = 0;
          else
            seg[node][i][j] = 1e9;
        }
      }
    }
    return;
  }
  build(start, (start + end) / 2, 2 * node);
  build((start + end) / 2 + 1, end, 2 * node + 1);
  for (int i = 0; i <= 4; i++) {
    for (int j = i; j <= 4; j++) {
      for (int k = i; k <= j; k++) {
        seg[node][i][j] =
            min(seg[node][i][j], seg[2 * node][i][k] + seg[2 * node + 1][k][j]);
      }
    }
  }
}
data query(int start, int end, int i, int j, int node) {
  if (start > j || end < i) {
    data x(normal_ret);
    return x;
  }
  if (start >= i && end <= j) {
    data x(seg[node]);
    return x;
  }
  data fi = query(start, (start + end) / 2, i, j, 2 * node);
  data si = query((start + end) / 2 + 1, end, i, j, 2 * node + 1);
  data ci;
  for (int i = 0; i < 5; i++) {
    for (int j = 0; j < 5; j++) ci.arr[i][j] = 1e9;
  }
  for (int i = 0; i <= 4; i++) {
    for (int j = i; j <= 4; j++) {
      for (int k = i; k <= j; k++) {
        ci.arr[i][j] = min(ci.arr[i][j], fi.arr[i][k] + si.arr[k][j]);
      }
    }
  }
  return ci;
}
int main() {
  for (int i = 0; i < (1 << 19); i++) {
    for (int j = 0; j < 5; j++) {
      for (int k = 0; k < 5; k++) {
        seg[i][j][k] = 1e9;
        normal_ret[j][k] = 1e9;
      }
    }
  }
  normal_ret[0][0] = normal_ret[4][4] = 0;
  ios_base::sync_with_stdio(0);
  cin >> n >> q;
  for (int i = 1; i <= n; i++) {
    char k;
    cin >> k;
    arr[i] = k - '0';
  }
  build(1, n, 1);
  for (int i = 0; i < q; i++) {
    int l, r;
    cin >> l >> r;
    data matrix = query(1, n, l, r, 1);
    if (matrix.arr[0][4] >= 1e8)
      cout << -1 << '\n';
    else
      cout << matrix.arr[0][4] << '\n';
  }
  return 0;
}

```