#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 10;
const int inf = 0x3f3f3f3f;
struct matrix {
  int c[5][5];
  inline void init() {
    for (int i = 0; i < 5; ++i)
      for (int j = 0; j < 5; ++j) c[i][j] = inf;
  }
};
matrix operator*(matrix A, matrix B) {
  matrix ret;
  for (int i = 0; i < 5; ++i) {
    for (int j = 0; j < 5; ++j) {
      ret.c[i][j] = inf;
      for (int k = 0; k < 5; ++k)
        ret.c[i][j] = min(ret.c[i][j], A.c[i][k] + B.c[k][j]);
    }
  }
  return ret;
}
int n, q;
char s[N];
namespace SGT {
const int M = N << 2;
matrix tr[M];
inline void init(int p, int l, int r) {
  if (l == r) {
    tr[p].init();
    tr[p].c[0][0] = tr[p].c[1][1] = tr[p].c[2][2] = tr[p].c[3][3] =
        tr[p].c[4][4] = 0;
    if (s[l] == '2')
      tr[p].c[0][0] = 1, tr[p].c[0][1] = 0;
    else if (s[l] == '0')
      tr[p].c[1][1] = 1, tr[p].c[1][2] = 0;
    else if (s[l] == '1')
      tr[p].c[2][2] = 1, tr[p].c[2][3] = 0;
    else if (s[l] == '7')
      tr[p].c[3][3] = 1, tr[p].c[3][4] = 0;
    else if (s[l] == '6')
      tr[p].c[3][3] = tr[p].c[4][4] = 1;
    return;
  }
  init((p << 1), l, ((l + r) >> 1));
  init((p << 1 | 1), ((l + r) >> 1) + 1, r);
  tr[p] = tr[(p << 1)] * tr[(p << 1 | 1)];
}
inline matrix query(int p, int l, int r, int ql, int qr) {
  if (ql <= l && r <= qr) return tr[p];
  if (ql > ((l + r) >> 1))
    return query((p << 1 | 1), ((l + r) >> 1) + 1, r, ql, qr);
  if (qr <= ((l + r) >> 1)) return query((p << 1), l, ((l + r) >> 1), ql, qr);
  return query((p << 1), l, ((l + r) >> 1), ql, qr) *
         query((p << 1 | 1), ((l + r) >> 1) + 1, r, ql, qr);
}
}  // namespace SGT
int main() {
  scanf("%d%d", &n, &q);
  scanf("%s", s + 1);
  SGT::init(1, 1, n);
  for (int i = 1, l, r; i <= q; ++i) {
    scanf("%d%d", &l, &r);
    int x = SGT::query(1, 1, n, l, r).c[0][4];
    printf("%d\n", x == inf ? -1 : x);
  }
  return 0;
}

### Prompt

Create a solution in cpp for 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 = 2e5 + 10;
const int inf = 0x3f3f3f3f;
struct matrix {
  int c[5][5];
  inline void init() {
    for (int i = 0; i < 5; ++i)
      for (int j = 0; j < 5; ++j) c[i][j] = inf;
  }
};
matrix operator*(matrix A, matrix B) {
  matrix ret;
  for (int i = 0; i < 5; ++i) {
    for (int j = 0; j < 5; ++j) {
      ret.c[i][j] = inf;
      for (int k = 0; k < 5; ++k)
        ret.c[i][j] = min(ret.c[i][j], A.c[i][k] + B.c[k][j]);
    }
  }
  return ret;
}
int n, q;
char s[N];
namespace SGT {
const int M = N << 2;
matrix tr[M];
inline void init(int p, int l, int r) {
  if (l == r) {
    tr[p].init();
    tr[p].c[0][0] = tr[p].c[1][1] = tr[p].c[2][2] = tr[p].c[3][3] =
        tr[p].c[4][4] = 0;
    if (s[l] == '2')
      tr[p].c[0][0] = 1, tr[p].c[0][1] = 0;
    else if (s[l] == '0')
      tr[p].c[1][1] = 1, tr[p].c[1][2] = 0;
    else if (s[l] == '1')
      tr[p].c[2][2] = 1, tr[p].c[2][3] = 0;
    else if (s[l] == '7')
      tr[p].c[3][3] = 1, tr[p].c[3][4] = 0;
    else if (s[l] == '6')
      tr[p].c[3][3] = tr[p].c[4][4] = 1;
    return;
  }
  init((p << 1), l, ((l + r) >> 1));
  init((p << 1 | 1), ((l + r) >> 1) + 1, r);
  tr[p] = tr[(p << 1)] * tr[(p << 1 | 1)];
}
inline matrix query(int p, int l, int r, int ql, int qr) {
  if (ql <= l && r <= qr) return tr[p];
  if (ql > ((l + r) >> 1))
    return query((p << 1 | 1), ((l + r) >> 1) + 1, r, ql, qr);
  if (qr <= ((l + r) >> 1)) return query((p << 1), l, ((l + r) >> 1), ql, qr);
  return query((p << 1), l, ((l + r) >> 1), ql, qr) *
         query((p << 1 | 1), ((l + r) >> 1) + 1, r, ql, qr);
}
}  // namespace SGT
int main() {
  scanf("%d%d", &n, &q);
  scanf("%s", s + 1);
  SGT::init(1, 1, n);
  for (int i = 1, l, r; i <= q; ++i) {
    scanf("%d%d", &l, &r);
    int x = SGT::query(1, 1, n, l, r).c[0][4];
    printf("%d\n", x == inf ? -1 : x);
  }
  return 0;
}

```