#include <bits/stdc++.h>
using namespace std;
const double eps = 1e-8;
const int INF = (1 << 30) - 1;
const int MAXN = 100010;
int n, q;
char s[200010];
struct Node {
  int s[5][5];
} DP[200010 << 2];
inline void Init(Node &dp) {
  for (int i = 0; i < 5; ++i)
    for (int j = 0; j < 5; ++j) dp.s[i][j] = 200000;
}
inline void Push_up(Node &dp, Node &dp1, Node &dp2) {
  Init(dp);
  for (int i = 0; i < 5; ++i) {
    for (int j = i; j < 5; ++j) {
      for (int k = i; k <= j; ++k) {
        dp.s[i][j] = min(dp.s[i][j], dp1.s[i][k] + dp2.s[k][j]);
      }
    }
  }
}
void Build(int p, int l, int r) {
  Init(DP[p]);
  if (l == r) {
    for (int i = 0; i < 5; ++i) DP[p].s[i][i] = 0;
    if (s[l] == '2')
      DP[p].s[0][1] = 0, DP[p].s[0][0] = 1;
    else if (s[l] == '0')
      DP[p].s[1][2] = 0, DP[p].s[1][1] = 1;
    else if (s[l] == '1')
      DP[p].s[2][3] = 0, DP[p].s[2][2] = 1;
    else if (s[l] == '6')
      DP[p].s[3][3] = 1, DP[p].s[4][4] = 1;
    else if (s[l] == '7')
      DP[p].s[3][4] = 0, DP[p].s[3][3] = 1;
    return;
  }
  int mid = ((l) + ((r) - (l)) / 2);
  Build(p << 1, l, mid);
  Build(p << 1 | 1, mid + 1, r);
  Push_up(DP[p], DP[p << 1], DP[p << 1 | 1]);
}
Node Query(int a, int b, int p, int l, int r) {
  if (a <= l && r <= b) return DP[p];
  int mid = ((l) + ((r) - (l)) / 2);
  Node res, L, R;
  bool fL = 0, fR = 0;
  if (a <= mid) fL = 1, L = Query(a, b, p << 1, l, mid);
  if (b > mid) fR = 1, R = Query(a, b, p << 1 | 1, mid + 1, r);
  if (fL) {
    if (fR) {
      Push_up(res, L, R);
      return res;
    } else
      return L;
  } else
    return R;
}
int main() {
  scanf("%d%d", &n, &q);
  scanf("%s", s + 1);
  Build(1, 1, n);
  for (int i = 1; i <= q; ++i) {
    int a, b;
    scanf("%d%d", &a, &b);
    Node res = Query(a, b, 1, 1, n);
    printf("%d\n", res.s[0][4] >= 200000 ? -1 : res.s[0][4]);
  }
  return 0;
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

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 double eps = 1e-8;
const int INF = (1 << 30) - 1;
const int MAXN = 100010;
int n, q;
char s[200010];
struct Node {
  int s[5][5];
} DP[200010 << 2];
inline void Init(Node &dp) {
  for (int i = 0; i < 5; ++i)
    for (int j = 0; j < 5; ++j) dp.s[i][j] = 200000;
}
inline void Push_up(Node &dp, Node &dp1, Node &dp2) {
  Init(dp);
  for (int i = 0; i < 5; ++i) {
    for (int j = i; j < 5; ++j) {
      for (int k = i; k <= j; ++k) {
        dp.s[i][j] = min(dp.s[i][j], dp1.s[i][k] + dp2.s[k][j]);
      }
    }
  }
}
void Build(int p, int l, int r) {
  Init(DP[p]);
  if (l == r) {
    for (int i = 0; i < 5; ++i) DP[p].s[i][i] = 0;
    if (s[l] == '2')
      DP[p].s[0][1] = 0, DP[p].s[0][0] = 1;
    else if (s[l] == '0')
      DP[p].s[1][2] = 0, DP[p].s[1][1] = 1;
    else if (s[l] == '1')
      DP[p].s[2][3] = 0, DP[p].s[2][2] = 1;
    else if (s[l] == '6')
      DP[p].s[3][3] = 1, DP[p].s[4][4] = 1;
    else if (s[l] == '7')
      DP[p].s[3][4] = 0, DP[p].s[3][3] = 1;
    return;
  }
  int mid = ((l) + ((r) - (l)) / 2);
  Build(p << 1, l, mid);
  Build(p << 1 | 1, mid + 1, r);
  Push_up(DP[p], DP[p << 1], DP[p << 1 | 1]);
}
Node Query(int a, int b, int p, int l, int r) {
  if (a <= l && r <= b) return DP[p];
  int mid = ((l) + ((r) - (l)) / 2);
  Node res, L, R;
  bool fL = 0, fR = 0;
  if (a <= mid) fL = 1, L = Query(a, b, p << 1, l, mid);
  if (b > mid) fR = 1, R = Query(a, b, p << 1 | 1, mid + 1, r);
  if (fL) {
    if (fR) {
      Push_up(res, L, R);
      return res;
    } else
      return L;
  } else
    return R;
}
int main() {
  scanf("%d%d", &n, &q);
  scanf("%s", s + 1);
  Build(1, 1, n);
  for (int i = 1; i <= q; ++i) {
    int a, b;
    scanf("%d%d", &a, &b);
    Node res = Query(a, b, 1, 1, n);
    printf("%d\n", res.s[0][4] >= 200000 ? -1 : res.s[0][4]);
  }
  return 0;
}

```