#include <bits/stdc++.h>
using namespace std;
void ga(int N, int *A) {
  for (int i(0); i < N; i++) scanf("%d", A + i);
}
char s[(1 << 18)];
int N, Q, w[] = {2, 0, 1, 7, -1}, W[] = {2, 0, 1, 6, 6}, a, b;
struct sX {
  int g[2 * (1 << 18)][5][5], N, H[5][5];
  void ini(int n) {
    N = 1 << (int(log2(n) - (1e-10)) + 1);
    st(1, 0, N - 1);
  }
  void st(int u, int B, int E) {
    if (B == E) {
      fill(&**g[u], &g[u][4][5], (1 << 29));
      for (int i(0); i < 5; i++) g[u][i][i] = s[B] - 48 == W[i];
      for (int i(0); i < 4; i++)
        if (s[B] - 48 == w[i]) g[u][i][i + 1] = 0;
      return;
    }
    st(u << 1, B, (B + E) >> 1), st(u << 1 | 1, (B + E) / 2 + 1, E);
    mg(g[u], g[u << 1], g[u << 1 | 1]);
  }
  void mg(int g[5][5], int a[5][5], int b[5][5]) {
    fill(&**g, &g[4][5], (1 << 29));
    for (int i(0); i < 5; i++)
      for (int k(i); k < 5; k++)
        for (int l(k); l < 5; l++) g[i][l] = min(g[i][l], a[i][k] + b[k][l]);
  }
  int gt(int b, int e) { return gt(b, e, 1, 0, N - 1, H), H[0][4]; }
  void gt(int b, int e, int u, int B, int E, int G[5][5]) {
    if (B > e || E < b) {
      fill(&**G, &G[4][5], (1 << 29));
      for (int i(0); i < 5; i++) G[i][i] = 0;
      return;
    }
    if (b <= B && e >= E) {
      for (int i(0); i < 5; i++)
        for (int j(0); j < 5; j++) G[i][j] = g[u][i][j];
      return;
    }
    int A[5][5], C[5][5];
    gt(b, e, u << 1, B, (B + E) >> 1, A),
        gt(b, e, u << 1 | 1, (B + E) / 2 + 1, E, C);
    mg(G, A, C);
  }
} T;
int main(void) {
  scanf("%d%d%s", &N, &Q, s), T.ini(N);
  for (int i(0); i < Q; i++) {
    scanf("%d%d", &a, &b);
    a = T.gt(a - 1, b - 1);
    printf("%d\n", a ^ (1 << 29) ? a : -1);
  }
  return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

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;
void ga(int N, int *A) {
  for (int i(0); i < N; i++) scanf("%d", A + i);
}
char s[(1 << 18)];
int N, Q, w[] = {2, 0, 1, 7, -1}, W[] = {2, 0, 1, 6, 6}, a, b;
struct sX {
  int g[2 * (1 << 18)][5][5], N, H[5][5];
  void ini(int n) {
    N = 1 << (int(log2(n) - (1e-10)) + 1);
    st(1, 0, N - 1);
  }
  void st(int u, int B, int E) {
    if (B == E) {
      fill(&**g[u], &g[u][4][5], (1 << 29));
      for (int i(0); i < 5; i++) g[u][i][i] = s[B] - 48 == W[i];
      for (int i(0); i < 4; i++)
        if (s[B] - 48 == w[i]) g[u][i][i + 1] = 0;
      return;
    }
    st(u << 1, B, (B + E) >> 1), st(u << 1 | 1, (B + E) / 2 + 1, E);
    mg(g[u], g[u << 1], g[u << 1 | 1]);
  }
  void mg(int g[5][5], int a[5][5], int b[5][5]) {
    fill(&**g, &g[4][5], (1 << 29));
    for (int i(0); i < 5; i++)
      for (int k(i); k < 5; k++)
        for (int l(k); l < 5; l++) g[i][l] = min(g[i][l], a[i][k] + b[k][l]);
  }
  int gt(int b, int e) { return gt(b, e, 1, 0, N - 1, H), H[0][4]; }
  void gt(int b, int e, int u, int B, int E, int G[5][5]) {
    if (B > e || E < b) {
      fill(&**G, &G[4][5], (1 << 29));
      for (int i(0); i < 5; i++) G[i][i] = 0;
      return;
    }
    if (b <= B && e >= E) {
      for (int i(0); i < 5; i++)
        for (int j(0); j < 5; j++) G[i][j] = g[u][i][j];
      return;
    }
    int A[5][5], C[5][5];
    gt(b, e, u << 1, B, (B + E) >> 1, A),
        gt(b, e, u << 1 | 1, (B + E) / 2 + 1, E, C);
    mg(G, A, C);
  }
} T;
int main(void) {
  scanf("%d%d%s", &N, &Q, s), T.ini(N);
  for (int i(0); i < Q; i++) {
    scanf("%d%d", &a, &b);
    a = T.gt(a - 1, b - 1);
    printf("%d\n", a ^ (1 << 29) ? a : -1);
  }
  return 0;
}

```