#include <bits/stdc++.h>
using namespace std;
const int N = 200001;
const int INF = 1061109567;
int n, q;
char s[N];
struct Matrix {
  int mat[5][5];
  Matrix() {
    memset(mat, 63, sizeof(mat));
    return;
  }
  Matrix operator=(const char &c) {
    for (int i = 0; i < 5; i++)
      for (int j = 0; j < 5; j++) mat[i][j] = (i == j) ? 0 : INF;
    if (c == '2') mat[0][1] = 0, mat[0][0] = 1;
    if (c == '0') mat[1][2] = 0, mat[1][1] = 1;
    if (c == '1') mat[2][3] = 0, mat[2][2] = 1;
    if (c == '7') mat[3][4] = 0, mat[3][3] = 1;
    if (c == '6') mat[3][3] = 1, mat[4][4] = 1;
    return *this;
  }
  Matrix operator*(const Matrix &b) const {
    Matrix res;
    for (int i = 0; i < 5; i++)
      for (int j = 0; j < 5; j++)
        for (int k = 0; k < 5; k++)
          res.mat[i][j] = min(res.mat[i][j], mat[i][k] + b.mat[k][j]);
    return res;
  }
};
struct Node {
  int l, r;
  Matrix sum;
} tree[N << 2];
void push_up(int i) {
  tree[i].sum = tree[i * 2].sum * tree[i * 2 + 1].sum;
  return;
}
void build(int i, int l, int r) {
  tree[i].l = l, tree[i].r = r;
  if (l == r) {
    tree[i].sum = s[l];
    return;
  }
  int mid = (l + r) / 2;
  build(i * 2, l, mid);
  build(i * 2 + 1, mid + 1, r);
  push_up(i);
  return;
}
Matrix query(int i, int L, int R) {
  if (L <= tree[i].l && tree[i].r <= R) return tree[i].sum;
  if (R <= tree[i * 2].r)
    return query(i * 2, L, R);
  else if (L >= tree[i * 2 + 1].l)
    return query(i * 2 + 1, L, R);
  else
    return query(i * 2, L, R) * query(i * 2 + 1, L, R);
}
int main() {
  scanf("%d%d%s", &n, &q, s + 1);
  build(1, 1, n);
  while (q--) {
    int l, r;
    scanf("%d%d", &l, &r);
    int ans = query(1, l, r).mat[0][4];
    if (ans >= INF) ans = -1;
    printf("%d\n", ans);
  }
  return 0;
}

### Prompt

Please formulate 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;
const int N = 200001;
const int INF = 1061109567;
int n, q;
char s[N];
struct Matrix {
  int mat[5][5];
  Matrix() {
    memset(mat, 63, sizeof(mat));
    return;
  }
  Matrix operator=(const char &c) {
    for (int i = 0; i < 5; i++)
      for (int j = 0; j < 5; j++) mat[i][j] = (i == j) ? 0 : INF;
    if (c == '2') mat[0][1] = 0, mat[0][0] = 1;
    if (c == '0') mat[1][2] = 0, mat[1][1] = 1;
    if (c == '1') mat[2][3] = 0, mat[2][2] = 1;
    if (c == '7') mat[3][4] = 0, mat[3][3] = 1;
    if (c == '6') mat[3][3] = 1, mat[4][4] = 1;
    return *this;
  }
  Matrix operator*(const Matrix &b) const {
    Matrix res;
    for (int i = 0; i < 5; i++)
      for (int j = 0; j < 5; j++)
        for (int k = 0; k < 5; k++)
          res.mat[i][j] = min(res.mat[i][j], mat[i][k] + b.mat[k][j]);
    return res;
  }
};
struct Node {
  int l, r;
  Matrix sum;
} tree[N << 2];
void push_up(int i) {
  tree[i].sum = tree[i * 2].sum * tree[i * 2 + 1].sum;
  return;
}
void build(int i, int l, int r) {
  tree[i].l = l, tree[i].r = r;
  if (l == r) {
    tree[i].sum = s[l];
    return;
  }
  int mid = (l + r) / 2;
  build(i * 2, l, mid);
  build(i * 2 + 1, mid + 1, r);
  push_up(i);
  return;
}
Matrix query(int i, int L, int R) {
  if (L <= tree[i].l && tree[i].r <= R) return tree[i].sum;
  if (R <= tree[i * 2].r)
    return query(i * 2, L, R);
  else if (L >= tree[i * 2 + 1].l)
    return query(i * 2 + 1, L, R);
  else
    return query(i * 2, L, R) * query(i * 2 + 1, L, R);
}
int main() {
  scanf("%d%d%s", &n, &q, s + 1);
  build(1, 1, n);
  while (q--) {
    int l, r;
    scanf("%d%d", &l, &r);
    int ans = query(1, l, r).mat[0][4];
    if (ans >= INF) ans = -1;
    printf("%d\n", ans);
  }
  return 0;
}

```