#include <bits/stdc++.h>
using namespace std;
const int MAXN = 2e5 + 5;
const int inf = 0x3f3f3f3f;
inline void chmin(int &a, int b) {
  if (a > b) a = b;
}
int n, q;
char str[MAXN];
struct MAT {
  int a[5][5];
  MAT(char c = '#') {
    memset(a, 0x3f, sizeof(a));
    if (c == '#') return;
    a[0][0] = a[1][1] = a[2][2] = a[3][3] = a[4][4] = 0;
    if (c == '2')
      a[0][0] = 1, a[0][1] = 0;
    else if (c == '0')
      a[1][1] = 1, a[1][2] = 0;
    else if (c == '1')
      a[2][2] = 1, a[2][3] = 0;
    else if (c == '7')
      a[3][3] = 1, a[3][4] = 0;
    else if (c == '6')
      a[3][3] = a[4][4] = 1;
  }
  MAT operator+(MAT b) {
    MAT res;
    for (int i = 0; i <= 4; i++)
      for (int j = i; j <= 4; j++)
        for (int k = i; k <= j; k++) chmin(res.a[i][j], a[i][k] + b.a[k][j]);
    return res;
  }
} seg[MAXN << 2];
inline void pushup(int rt) { seg[rt] = seg[rt << 1] + seg[rt << 1 | 1]; }
inline void build(int l, int r, int rt) {
  if (l == r) {
    seg[rt] = MAT(str[l]);
    return;
  }
  int m = l + r >> 1;
  build(l, m, rt << 1);
  build(m + 1, r, rt << 1 | 1);
  pushup(rt);
}
inline MAT query(int L, int R, int l, int r, int rt) {
  if (L <= l && R >= r) return seg[rt];
  int m = l + r >> 1;
  if (R <= m) return query(L, R, l, m, rt << 1);
  if (L > m) return query(L, R, m + 1, r, rt << 1 | 1);
  return query(L, R, l, m, rt << 1) + query(L, R, m + 1, r, rt << 1 | 1);
}
int main() {
  int l, r;
  MAT res;
  scanf("%d%d%s", &n, &q, str + 1);
  build(1, n, 1);
  while (q--) {
    scanf("%d%d", &l, &r);
    res = query(l, r, 1, n, 1);
    printf("%d\n", res.a[0][4] == inf ? -1 : res.a[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;
const int MAXN = 2e5 + 5;
const int inf = 0x3f3f3f3f;
inline void chmin(int &a, int b) {
  if (a > b) a = b;
}
int n, q;
char str[MAXN];
struct MAT {
  int a[5][5];
  MAT(char c = '#') {
    memset(a, 0x3f, sizeof(a));
    if (c == '#') return;
    a[0][0] = a[1][1] = a[2][2] = a[3][3] = a[4][4] = 0;
    if (c == '2')
      a[0][0] = 1, a[0][1] = 0;
    else if (c == '0')
      a[1][1] = 1, a[1][2] = 0;
    else if (c == '1')
      a[2][2] = 1, a[2][3] = 0;
    else if (c == '7')
      a[3][3] = 1, a[3][4] = 0;
    else if (c == '6')
      a[3][3] = a[4][4] = 1;
  }
  MAT operator+(MAT b) {
    MAT res;
    for (int i = 0; i <= 4; i++)
      for (int j = i; j <= 4; j++)
        for (int k = i; k <= j; k++) chmin(res.a[i][j], a[i][k] + b.a[k][j]);
    return res;
  }
} seg[MAXN << 2];
inline void pushup(int rt) { seg[rt] = seg[rt << 1] + seg[rt << 1 | 1]; }
inline void build(int l, int r, int rt) {
  if (l == r) {
    seg[rt] = MAT(str[l]);
    return;
  }
  int m = l + r >> 1;
  build(l, m, rt << 1);
  build(m + 1, r, rt << 1 | 1);
  pushup(rt);
}
inline MAT query(int L, int R, int l, int r, int rt) {
  if (L <= l && R >= r) return seg[rt];
  int m = l + r >> 1;
  if (R <= m) return query(L, R, l, m, rt << 1);
  if (L > m) return query(L, R, m + 1, r, rt << 1 | 1);
  return query(L, R, l, m, rt << 1) + query(L, R, m + 1, r, rt << 1 | 1);
}
int main() {
  int l, r;
  MAT res;
  scanf("%d%d%s", &n, &q, str + 1);
  build(1, n, 1);
  while (q--) {
    scanf("%d%d", &l, &r);
    res = query(l, r, 1, n, 1);
    printf("%d\n", res.a[0][4] == inf ? -1 : res.a[0][4]);
  }
  return 0;
}

```