#include <bits/stdc++.h>
using namespace std;
int N, Q;
char S[200005];
int Arb[200005 * 4][5][5];
int Partial[12][200005];
int Res[5][5], Res2[5][5];
const int INF = 1000000005;
void copy(int A[][5], int B[][5]) {
  for (int i = 0; i < 5; i++)
    for (int j = 0; j < 5; j++) B[i][j] = A[i][j];
}
void mergeNodes(int A[][5], int B[][5], int C[][5]) {
  for (int i = 0; i < 5; i++) {
    for (int j = i; j < 5; j++) {
      C[i][j] = INF;
      for (int k = i; k <= j; k++) {
        C[i][j] = min(C[i][j], A[i][k] + B[k][j]);
      }
    }
  }
}
void Read() {
  scanf("%d%d", &N, &Q);
  scanf("%s", S + 1);
}
void buildTree(int K, int L, int R) {
  if (L == R) {
    for (int i = 0; i < 5; i++)
      for (int j = 0; j < 5; j++) Arb[K][i][j] = INF;
    for (int i = 0; i < 5; i++) Arb[K][i][i] = 0;
    if (S[L] == '2') {
      Arb[K][0][0] = 1;
      Arb[K][0][1] = 0;
      return;
    }
    if (S[L] == '0') {
      Arb[K][1][2] = 0;
      Arb[K][1][1] = 1;
      return;
    }
    if (S[L] == '1') {
      Arb[K][2][2] = 1;
      Arb[K][2][3] = 0;
      return;
    }
    if (S[L] == '7') {
      Arb[K][3][3] = 1;
      Arb[K][3][4] = 0;
      return;
    }
    if (S[L] == '6') {
      Arb[K][3][3] = 1;
      Arb[K][4][4] = 1;
      return;
    }
    return;
  }
  buildTree(K * 2, L, (L + R) / 2);
  buildTree(K * 2 + 1, (L + R) / 2 + 1, R);
  mergeNodes(Arb[K * 2], Arb[K * 2 + 1], Arb[K]);
}
void query(int K, int L, int R, int x, int y) {
  if (L > R || R < x || L > y) return;
  if (L >= x && R <= y) {
    copy(Res, Res2);
    mergeNodes(Res2, Arb[K], Res);
    return;
  }
  query(K * 2, L, (L + R) / 2, x, y);
  query(K * 2 + 1, (L + R) / 2 + 1, R, x, y);
}
void init(int A[][5]) {
  for (int i = 0; i < 5; i++)
    for (int j = 0; j < 5; j++) A[i][j] = INF;
  A[0][0] = 0;
}
int main() {
  Read();
  buildTree(1, 1, N);
  for (int i = 1; i <= Q; i++) {
    int x, y;
    scanf("%d%d", &x, &y);
    init(Res);
    query(1, 1, N, x, y);
    if (Res[0][4] == INF) Res[0][4] = -1;
    printf("%d\n", Res[0][4]);
  }
  return 0;
}

### Prompt

Generate a cpp solution to 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;
int N, Q;
char S[200005];
int Arb[200005 * 4][5][5];
int Partial[12][200005];
int Res[5][5], Res2[5][5];
const int INF = 1000000005;
void copy(int A[][5], int B[][5]) {
  for (int i = 0; i < 5; i++)
    for (int j = 0; j < 5; j++) B[i][j] = A[i][j];
}
void mergeNodes(int A[][5], int B[][5], int C[][5]) {
  for (int i = 0; i < 5; i++) {
    for (int j = i; j < 5; j++) {
      C[i][j] = INF;
      for (int k = i; k <= j; k++) {
        C[i][j] = min(C[i][j], A[i][k] + B[k][j]);
      }
    }
  }
}
void Read() {
  scanf("%d%d", &N, &Q);
  scanf("%s", S + 1);
}
void buildTree(int K, int L, int R) {
  if (L == R) {
    for (int i = 0; i < 5; i++)
      for (int j = 0; j < 5; j++) Arb[K][i][j] = INF;
    for (int i = 0; i < 5; i++) Arb[K][i][i] = 0;
    if (S[L] == '2') {
      Arb[K][0][0] = 1;
      Arb[K][0][1] = 0;
      return;
    }
    if (S[L] == '0') {
      Arb[K][1][2] = 0;
      Arb[K][1][1] = 1;
      return;
    }
    if (S[L] == '1') {
      Arb[K][2][2] = 1;
      Arb[K][2][3] = 0;
      return;
    }
    if (S[L] == '7') {
      Arb[K][3][3] = 1;
      Arb[K][3][4] = 0;
      return;
    }
    if (S[L] == '6') {
      Arb[K][3][3] = 1;
      Arb[K][4][4] = 1;
      return;
    }
    return;
  }
  buildTree(K * 2, L, (L + R) / 2);
  buildTree(K * 2 + 1, (L + R) / 2 + 1, R);
  mergeNodes(Arb[K * 2], Arb[K * 2 + 1], Arb[K]);
}
void query(int K, int L, int R, int x, int y) {
  if (L > R || R < x || L > y) return;
  if (L >= x && R <= y) {
    copy(Res, Res2);
    mergeNodes(Res2, Arb[K], Res);
    return;
  }
  query(K * 2, L, (L + R) / 2, x, y);
  query(K * 2 + 1, (L + R) / 2 + 1, R, x, y);
}
void init(int A[][5]) {
  for (int i = 0; i < 5; i++)
    for (int j = 0; j < 5; j++) A[i][j] = INF;
  A[0][0] = 0;
}
int main() {
  Read();
  buildTree(1, 1, N);
  for (int i = 1; i <= Q; i++) {
    int x, y;
    scanf("%d%d", &x, &y);
    init(Res);
    query(1, 1, N, x, y);
    if (Res[0][4] == INF) Res[0][4] = -1;
    printf("%d\n", Res[0][4]);
  }
  return 0;
}

```