#include <bits/stdc++.h>
using namespace std;
const int inf = 1e9;
struct Matrix {
  int m[5][5];
} Tree[200010 << 2];
char s[200010];
int n, m;
Matrix merge(Matrix a, Matrix b) {
  Matrix c;
  for (int i = 0; i < 5; i++)
    for (int j = 0; j < 5; j++) c.m[i][j] = inf;
  for (int i = 0; i < 5; i++) {
    for (int j = i; j < 5; j++) {
      c.m[i][j] = inf;
      for (int k = i; k <= j; k++)
        c.m[i][j] = min(c.m[i][j], a.m[i][k] + b.m[k][j]);
    }
  }
  return c;
}
void build(int nl, int nr, int nth) {
  if (nl == nr) {
    Matrix &t = Tree[nth];
    for (int i = 0; i < 5; i++)
      for (int j = 0; j < 5; j++)
        if (i == j)
          t.m[i][j] = 0;
        else
          t.m[i][j] = inf;
    if (s[nl - 1] == '2') t.m[0][1] = 0, t.m[0][0] = 1;
    if (s[nl - 1] == '0') t.m[1][2] = 0, t.m[1][1] = 1;
    if (s[nl - 1] == '1') t.m[2][3] = 0, t.m[2][2] = 1;
    if (s[nl - 1] == '7') t.m[3][4] = 0, t.m[3][3] = 1;
    if (s[nl - 1] == '6') t.m[3][3] = 1, t.m[4][4] = 1;
    return;
  }
  int mid = (nl + nr) >> 1;
  build(nl, mid, nth << 1);
  build(mid + 1, nr, (nth << 1) | 1);
  Tree[nth] = merge(Tree[nth << 1], Tree[(nth << 1) | 1]);
}
Matrix qry(int l, int r, int nl, int nr, int nth) {
  if (l == nl && r == nr) return Tree[nth];
  int mid = (nl + nr) >> 1;
  if (l > mid)
    return qry(l, r, mid + 1, nr, (nth << 1) | 1);
  else if (r <= mid)
    return qry(l, r, nl, mid, nth << 1);
  else
    return merge(qry(l, mid, nl, mid, nth << 1),
                 qry(mid + 1, r, mid + 1, nr, (nth << 1) | 1));
}
int main() {
  scanf("%d%d", &n, &m);
  scanf("%s", s);
  build(1, n, 1);
  for (int i = 0; i < m; i++) {
    int l, r, ans;
    scanf("%d%d", &l, &r);
    ans = qry(l, r, 1, n, 1).m[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 inf = 1e9;
struct Matrix {
  int m[5][5];
} Tree[200010 << 2];
char s[200010];
int n, m;
Matrix merge(Matrix a, Matrix b) {
  Matrix c;
  for (int i = 0; i < 5; i++)
    for (int j = 0; j < 5; j++) c.m[i][j] = inf;
  for (int i = 0; i < 5; i++) {
    for (int j = i; j < 5; j++) {
      c.m[i][j] = inf;
      for (int k = i; k <= j; k++)
        c.m[i][j] = min(c.m[i][j], a.m[i][k] + b.m[k][j]);
    }
  }
  return c;
}
void build(int nl, int nr, int nth) {
  if (nl == nr) {
    Matrix &t = Tree[nth];
    for (int i = 0; i < 5; i++)
      for (int j = 0; j < 5; j++)
        if (i == j)
          t.m[i][j] = 0;
        else
          t.m[i][j] = inf;
    if (s[nl - 1] == '2') t.m[0][1] = 0, t.m[0][0] = 1;
    if (s[nl - 1] == '0') t.m[1][2] = 0, t.m[1][1] = 1;
    if (s[nl - 1] == '1') t.m[2][3] = 0, t.m[2][2] = 1;
    if (s[nl - 1] == '7') t.m[3][4] = 0, t.m[3][3] = 1;
    if (s[nl - 1] == '6') t.m[3][3] = 1, t.m[4][4] = 1;
    return;
  }
  int mid = (nl + nr) >> 1;
  build(nl, mid, nth << 1);
  build(mid + 1, nr, (nth << 1) | 1);
  Tree[nth] = merge(Tree[nth << 1], Tree[(nth << 1) | 1]);
}
Matrix qry(int l, int r, int nl, int nr, int nth) {
  if (l == nl && r == nr) return Tree[nth];
  int mid = (nl + nr) >> 1;
  if (l > mid)
    return qry(l, r, mid + 1, nr, (nth << 1) | 1);
  else if (r <= mid)
    return qry(l, r, nl, mid, nth << 1);
  else
    return merge(qry(l, mid, nl, mid, nth << 1),
                 qry(mid + 1, r, mid + 1, nr, (nth << 1) | 1));
}
int main() {
  scanf("%d%d", &n, &m);
  scanf("%s", s);
  build(1, n, 1);
  for (int i = 0; i < m; i++) {
    int l, r, ans;
    scanf("%d%d", &l, &r);
    ans = qry(l, r, 1, n, 1).m[0][4];
    if (ans == inf) ans = -1;
    printf("%d\n", ans);
  }
  return 0;
}

```