#include <bits/stdc++.h>
using namespace std;
const char *C1 = "2017", *C2 = "2016";
char S[200001];
struct node {
  int moves[5][5];
  void merge(node& ls, node& rs) {
    for (int a = 0; a < int(5); a++)
      for (int b = a; b < int(5); b++) {
        int& ans = moves[a][b];
        ans = INT_MAX;
        for (int p = a; p < int(b + 1); p++) {
          int lmoves = ls.moves[a][p];
          int rmoves = rs.moves[p][b];
          if (lmoves == INT_MAX || rmoves == INT_MAX) continue;
          ans = min(ans, lmoves + rmoves);
        }
      }
  }
} seg[800000];
void segBuild(int n, int l, int r) {
  if (l == r) {
    for (int a = 0; a < int(5); a++)
      for (int b = a; b < int(5); b++) {
        int& ans = seg[n].moves[a][b];
        ans = INT_MAX;
        char fc = C2[min(b, 3)];
        int add = (S[l] == fc) ? 1 : 0;
        if (a == b) {
          ans = add;
        } else if (a + 1 == b) {
          if (S[l] == C1[a]) ans = 0;
        }
      }
    return;
  }
  int m = (l + r) / 2;
  segBuild(2 * n + 1, l, m);
  segBuild(2 * n + 2, m + 1, r);
  seg[n].merge(seg[2 * n + 1], seg[2 * n + 2]);
}
node segQuery(int n, int l, int r, int i, int j) {
  if (i <= l && r <= j) return seg[n];
  int m = (l + r) / 2;
  if (m < i) return segQuery(2 * n + 2, m + 1, r, i, j);
  if (m >= j) return segQuery(2 * n + 1, l, m, i, j);
  node ls = segQuery(2 * n + 1, l, m, i, j);
  node rs = segQuery(2 * n + 2, m + 1, r, i, j);
  node a;
  a.merge(ls, rs);
  return a;
}
int main() {
  int N, Q;
  scanf("%d%d%s", &N, &Q, S);
  segBuild(0, 0, N - 1);
  for (int q = 0; q < int(Q); q++) {
    int a, b;
    scanf("%d%d", &a, &b);
    --a;
    --b;
    int ans = segQuery(0, 0, N - 1, a, b).moves[0][4];
    if (ans == INT_MAX) ans = -1;
    printf("%d\n", ans);
  }
}

### Prompt

Create a solution in cpp for 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 char *C1 = "2017", *C2 = "2016";
char S[200001];
struct node {
  int moves[5][5];
  void merge(node& ls, node& rs) {
    for (int a = 0; a < int(5); a++)
      for (int b = a; b < int(5); b++) {
        int& ans = moves[a][b];
        ans = INT_MAX;
        for (int p = a; p < int(b + 1); p++) {
          int lmoves = ls.moves[a][p];
          int rmoves = rs.moves[p][b];
          if (lmoves == INT_MAX || rmoves == INT_MAX) continue;
          ans = min(ans, lmoves + rmoves);
        }
      }
  }
} seg[800000];
void segBuild(int n, int l, int r) {
  if (l == r) {
    for (int a = 0; a < int(5); a++)
      for (int b = a; b < int(5); b++) {
        int& ans = seg[n].moves[a][b];
        ans = INT_MAX;
        char fc = C2[min(b, 3)];
        int add = (S[l] == fc) ? 1 : 0;
        if (a == b) {
          ans = add;
        } else if (a + 1 == b) {
          if (S[l] == C1[a]) ans = 0;
        }
      }
    return;
  }
  int m = (l + r) / 2;
  segBuild(2 * n + 1, l, m);
  segBuild(2 * n + 2, m + 1, r);
  seg[n].merge(seg[2 * n + 1], seg[2 * n + 2]);
}
node segQuery(int n, int l, int r, int i, int j) {
  if (i <= l && r <= j) return seg[n];
  int m = (l + r) / 2;
  if (m < i) return segQuery(2 * n + 2, m + 1, r, i, j);
  if (m >= j) return segQuery(2 * n + 1, l, m, i, j);
  node ls = segQuery(2 * n + 1, l, m, i, j);
  node rs = segQuery(2 * n + 2, m + 1, r, i, j);
  node a;
  a.merge(ls, rs);
  return a;
}
int main() {
  int N, Q;
  scanf("%d%d%s", &N, &Q, S);
  segBuild(0, 0, N - 1);
  for (int q = 0; q < int(Q); q++) {
    int a, b;
    scanf("%d%d", &a, &b);
    --a;
    --b;
    int ans = segQuery(0, 0, N - 1, a, b).moves[0][4];
    if (ans == INT_MAX) ans = -1;
    printf("%d\n", ans);
  }
}

```