#include <bits/stdc++.h>
using namespace std;
const int N = 200000 + 5;
struct Matrix {
  int a[5][5];
  Matrix operator*(const Matrix& ot) {
    Matrix rtn;
    for (int i = 0; i < 5; ++i) {
      for (int j = 0; j < 5; ++j) {
        rtn.a[i][j] = 100000000;
        for (int k = 0; k < 5; ++k) {
          rtn.a[i][j] = min(rtn.a[i][j], a[i][k] + ot.a[k][j]);
        }
      }
    }
    return rtn;
  }
};
struct Node {
  int l, r, rt;
  Matrix m;
} node[N << 2];
char s[N];
void build(int l, int r, int rt) {
  if (l == r) {
    for (int i = 0; i < 5; ++i) {
      for (int j = 0; j < 5; ++j) {
        node[rt].m.a[i][j] = 100000000;
        if (i == j) node[rt].m.a[i][j] = 0;
      }
    }
    if (s[l] == '2') node[rt].m.a[0][0] = 1, node[rt].m.a[0][1] = 0;
    if (s[l] == '0') node[rt].m.a[1][1] = 1, node[rt].m.a[1][2] = 0;
    if (s[l] == '1') node[rt].m.a[2][2] = 1, node[rt].m.a[2][3] = 0;
    if (s[l] == '7') node[rt].m.a[3][3] = 1, node[rt].m.a[3][4] = 0;
    if (s[l] == '6') node[rt].m.a[3][3] = 1, node[rt].m.a[4][4] = 1;
    return;
  }
  int mid = (l + r) >> 1;
  build(l, mid, rt << 1);
  build(mid + 1, r, rt << 1 | 1);
  node[rt].m = node[rt << 1].m * node[rt << 1 | 1].m;
}
Matrix query(int L, int R, int l, int r, int rt) {
  if (L <= l && r <= R) return node[rt].m;
  int mid = (l + r) >> 1;
  Matrix rtn;
  for (int i = 0; i < 5; ++i) {
    for (int j = 0; j < 5; ++j) rtn.a[i][j] = 100000000;
    rtn.a[i][i] = 0;
  }
  if (L <= mid) rtn = rtn * query(L, R, l, mid, rt << 1);
  if (mid < R) rtn = rtn * query(L, R, mid + 1, r, rt << 1 | 1);
  return rtn;
}
void solve() {
  int n, m;
  scanf("%d%d%s", &n, &m, s + 1);
  build(1, n, 1);
  for (; m; --m) {
    int l, r;
    scanf("%d%d", &l, &r);
    Matrix qr = query(l, r, 1, n, 1);
    if (qr.a[0][4] >= 100000000)
      puts("-1");
    else
      printf("%d\n", qr.a[0][4]);
  }
}
int main() {
  solve();
  return 0;
}

### Prompt

Please create a solution in cpp 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;
const int N = 200000 + 5;
struct Matrix {
  int a[5][5];
  Matrix operator*(const Matrix& ot) {
    Matrix rtn;
    for (int i = 0; i < 5; ++i) {
      for (int j = 0; j < 5; ++j) {
        rtn.a[i][j] = 100000000;
        for (int k = 0; k < 5; ++k) {
          rtn.a[i][j] = min(rtn.a[i][j], a[i][k] + ot.a[k][j]);
        }
      }
    }
    return rtn;
  }
};
struct Node {
  int l, r, rt;
  Matrix m;
} node[N << 2];
char s[N];
void build(int l, int r, int rt) {
  if (l == r) {
    for (int i = 0; i < 5; ++i) {
      for (int j = 0; j < 5; ++j) {
        node[rt].m.a[i][j] = 100000000;
        if (i == j) node[rt].m.a[i][j] = 0;
      }
    }
    if (s[l] == '2') node[rt].m.a[0][0] = 1, node[rt].m.a[0][1] = 0;
    if (s[l] == '0') node[rt].m.a[1][1] = 1, node[rt].m.a[1][2] = 0;
    if (s[l] == '1') node[rt].m.a[2][2] = 1, node[rt].m.a[2][3] = 0;
    if (s[l] == '7') node[rt].m.a[3][3] = 1, node[rt].m.a[3][4] = 0;
    if (s[l] == '6') node[rt].m.a[3][3] = 1, node[rt].m.a[4][4] = 1;
    return;
  }
  int mid = (l + r) >> 1;
  build(l, mid, rt << 1);
  build(mid + 1, r, rt << 1 | 1);
  node[rt].m = node[rt << 1].m * node[rt << 1 | 1].m;
}
Matrix query(int L, int R, int l, int r, int rt) {
  if (L <= l && r <= R) return node[rt].m;
  int mid = (l + r) >> 1;
  Matrix rtn;
  for (int i = 0; i < 5; ++i) {
    for (int j = 0; j < 5; ++j) rtn.a[i][j] = 100000000;
    rtn.a[i][i] = 0;
  }
  if (L <= mid) rtn = rtn * query(L, R, l, mid, rt << 1);
  if (mid < R) rtn = rtn * query(L, R, mid + 1, r, rt << 1 | 1);
  return rtn;
}
void solve() {
  int n, m;
  scanf("%d%d%s", &n, &m, s + 1);
  build(1, n, 1);
  for (; m; --m) {
    int l, r;
    scanf("%d%d", &l, &r);
    Matrix qr = query(l, r, 1, n, 1);
    if (qr.a[0][4] >= 100000000)
      puts("-1");
    else
      printf("%d\n", qr.a[0][4]);
  }
}
int main() {
  solve();
  return 0;
}

```