#include <bits/stdc++.h>
using namespace std;
const int N = 200005;
const int INF = 500000000;
const int nums[5] = {2, 0, 1, 7, 6};
struct node {
  int a[6][6];
  node operator+(const node& b) {
    node ans;
    for (int i = 0; i < 6; i++)
      for (int j = 0; j < 6; j++) ans.a[i][j] = INF;
    for (int i = 0; i < 6; i++)
      for (int j = i; j < 6; j++)
        for (int k = j; k < 6; k++)
          ans.a[i][k] = min(ans.a[i][k], a[i][j] + b.a[j][k]);
    return ans;
  }
};
int n, pw2;
node t[N * 4];
char s[N];
void initztr(int id, int val) {
  for (int i = 0; i < 6; i++) t[id].a[i][i] = 1;
  for (int i = 0; i < 6; i++) {
    if (i != 3) {
      if (nums[i] == val)
        t[id].a[i][i + 1] = 0;
      else
        t[id].a[i][i] = 0;
    } else {
      if (val == 6)
        t[id].a[3][5] = 0;
      else if (val == 7)
        t[id].a[3][4] = 0;
      else
        t[id].a[3][3] = 0;
    }
  }
}
node query(int l, int r) {
  node ans, ansr;
  bool flag = true, flagr = true;
  for (l += pw2, r += pw2; l < r; l >>= 1, r >>= 1) {
    if (l & 1) {
      if (flag)
        ans = t[l++], flag = false;
      else
        ans = ans + t[l++];
    }
    if (r & 1) {
      if (flagr)
        ansr = t[--r], flagr = false;
      else
        ansr = t[--r] + ansr;
    }
  }
  if (flag)
    return ansr;
  else if (flagr)
    return ans;
  return ans + ansr;
}
int main() {
  int q;
  node ans;
  scanf("%d%d", &n, &q);
  scanf("%s", s);
  for (pw2 = 1; pw2 < n; pw2 *= 2)
    ;
  for (int i = 1; i < pw2 * 2; i++) {
    for (int j = 0; j < 6; j++)
      for (int k = 0; k < 6; k++) t[i].a[j][k] = INF;
  }
  for (int i = pw2; i < pw2 + n; i++) initztr(i, s[i - pw2] - '0');
  for (int i = pw2 - 1; i > 0; i--) t[i] = t[i * 2] + t[i * 2 + 1];
  while (q--) {
    int l, r;
    scanf("%d%d", &l, &r);
    l--;
    ans = query(l, r);
    if (ans.a[0][4] != INF)
      printf("%d\n", ans.a[0][4]);
    else
      puts("-1");
  }
  return 0;
}

### Prompt

Develop a solution in CPP 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 int N = 200005;
const int INF = 500000000;
const int nums[5] = {2, 0, 1, 7, 6};
struct node {
  int a[6][6];
  node operator+(const node& b) {
    node ans;
    for (int i = 0; i < 6; i++)
      for (int j = 0; j < 6; j++) ans.a[i][j] = INF;
    for (int i = 0; i < 6; i++)
      for (int j = i; j < 6; j++)
        for (int k = j; k < 6; k++)
          ans.a[i][k] = min(ans.a[i][k], a[i][j] + b.a[j][k]);
    return ans;
  }
};
int n, pw2;
node t[N * 4];
char s[N];
void initztr(int id, int val) {
  for (int i = 0; i < 6; i++) t[id].a[i][i] = 1;
  for (int i = 0; i < 6; i++) {
    if (i != 3) {
      if (nums[i] == val)
        t[id].a[i][i + 1] = 0;
      else
        t[id].a[i][i] = 0;
    } else {
      if (val == 6)
        t[id].a[3][5] = 0;
      else if (val == 7)
        t[id].a[3][4] = 0;
      else
        t[id].a[3][3] = 0;
    }
  }
}
node query(int l, int r) {
  node ans, ansr;
  bool flag = true, flagr = true;
  for (l += pw2, r += pw2; l < r; l >>= 1, r >>= 1) {
    if (l & 1) {
      if (flag)
        ans = t[l++], flag = false;
      else
        ans = ans + t[l++];
    }
    if (r & 1) {
      if (flagr)
        ansr = t[--r], flagr = false;
      else
        ansr = t[--r] + ansr;
    }
  }
  if (flag)
    return ansr;
  else if (flagr)
    return ans;
  return ans + ansr;
}
int main() {
  int q;
  node ans;
  scanf("%d%d", &n, &q);
  scanf("%s", s);
  for (pw2 = 1; pw2 < n; pw2 *= 2)
    ;
  for (int i = 1; i < pw2 * 2; i++) {
    for (int j = 0; j < 6; j++)
      for (int k = 0; k < 6; k++) t[i].a[j][k] = INF;
  }
  for (int i = pw2; i < pw2 + n; i++) initztr(i, s[i - pw2] - '0');
  for (int i = pw2 - 1; i > 0; i--) t[i] = t[i * 2] + t[i * 2 + 1];
  while (q--) {
    int l, r;
    scanf("%d%d", &l, &r);
    l--;
    ans = query(l, r);
    if (ans.a[0][4] != INF)
      printf("%d\n", ans.a[0][4]);
    else
      puts("-1");
  }
  return 0;
}

```