#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 10;
const long long mod = 1e9 + 7;
int n, m;
char c[maxn];
struct mmp {
  int a[5][5];
  void init0() {
    for (int i = 0; i <= 4; i++)
      for (int j = 0; j <= 4; j++) a[i][j] = n;
  }
  void init1() {
    for (int i = 0; i <= 4; i++) a[i][i] = 0;
  }
  void init2(char c) {
    if (c == '2') {
      a[0][0] = 1;
      a[0][1] = 0;
    }
    if (c == '0') {
      a[1][1] = 1;
      a[1][2] = 0;
    }
    if (c == '1') {
      a[2][2] = 1;
      a[2][3] = 0;
    }
    if (c == '7') {
      a[3][3] = 1;
      a[3][4] = 0;
    }
    if (c == '6') {
      a[4][4] = 1;
      a[3][3] = 1;
    }
  }
  mmp cmb(mmp x) {
    mmp ret;
    ret.init0();
    for (int j = 0; j <= 4; j++)
      for (int i = 0; i <= 4; i++)
        for (int k = 0; k <= 4; k++)
          ret.a[i][k] = min(ret.a[i][k], a[i][j] + x.a[j][k]);
    return ret;
  }
} tr[maxn * 4];
void build(int num, int l, int r) {
  if (l == r) {
    tr[num].init0();
    tr[num].init1();
    tr[num].init2(c[l]);
    return;
  }
  int mid = (l + r) / 2;
  build(num * 2, l, mid);
  build(num * 2 + 1, mid + 1, r);
  tr[num] = tr[num * 2].cmb(tr[num * 2 + 1]);
}
mmp getout(int num, int l, int r, int x, int y) {
  if (x <= l && r <= y) return tr[num];
  int mid = (l + r) / 2;
  if (y <= mid)
    return getout(num * 2, l, mid, x, y);
  else if (x >= mid + 1)
    return getout(num * 2 + 1, mid + 1, r, x, y);
  else {
    mmp ret;
    ret.init0();
    ret.init1();
    ret = ret.cmb(getout(num * 2, l, mid, x, y));
    ret = ret.cmb(getout(num * 2 + 1, mid + 1, r, x, y));
    return ret;
  }
}
int main() {
  int i, j;
  cin >> n >> m;
  scanf("%s", c + 1);
  build(1, 1, n);
  while (m--) {
    scanf("%d%d", &i, &j);
    mmp ret = getout(1, 1, n, i, j);
    printf("%d\n", (ret.a[0][4] < n ? ret.a[0][4] : -1));
  }
  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 int maxn = 2e5 + 10;
const long long mod = 1e9 + 7;
int n, m;
char c[maxn];
struct mmp {
  int a[5][5];
  void init0() {
    for (int i = 0; i <= 4; i++)
      for (int j = 0; j <= 4; j++) a[i][j] = n;
  }
  void init1() {
    for (int i = 0; i <= 4; i++) a[i][i] = 0;
  }
  void init2(char c) {
    if (c == '2') {
      a[0][0] = 1;
      a[0][1] = 0;
    }
    if (c == '0') {
      a[1][1] = 1;
      a[1][2] = 0;
    }
    if (c == '1') {
      a[2][2] = 1;
      a[2][3] = 0;
    }
    if (c == '7') {
      a[3][3] = 1;
      a[3][4] = 0;
    }
    if (c == '6') {
      a[4][4] = 1;
      a[3][3] = 1;
    }
  }
  mmp cmb(mmp x) {
    mmp ret;
    ret.init0();
    for (int j = 0; j <= 4; j++)
      for (int i = 0; i <= 4; i++)
        for (int k = 0; k <= 4; k++)
          ret.a[i][k] = min(ret.a[i][k], a[i][j] + x.a[j][k]);
    return ret;
  }
} tr[maxn * 4];
void build(int num, int l, int r) {
  if (l == r) {
    tr[num].init0();
    tr[num].init1();
    tr[num].init2(c[l]);
    return;
  }
  int mid = (l + r) / 2;
  build(num * 2, l, mid);
  build(num * 2 + 1, mid + 1, r);
  tr[num] = tr[num * 2].cmb(tr[num * 2 + 1]);
}
mmp getout(int num, int l, int r, int x, int y) {
  if (x <= l && r <= y) return tr[num];
  int mid = (l + r) / 2;
  if (y <= mid)
    return getout(num * 2, l, mid, x, y);
  else if (x >= mid + 1)
    return getout(num * 2 + 1, mid + 1, r, x, y);
  else {
    mmp ret;
    ret.init0();
    ret.init1();
    ret = ret.cmb(getout(num * 2, l, mid, x, y));
    ret = ret.cmb(getout(num * 2 + 1, mid + 1, r, x, y));
    return ret;
  }
}
int main() {
  int i, j;
  cin >> n >> m;
  scanf("%s", c + 1);
  build(1, 1, n);
  while (m--) {
    scanf("%d%d", &i, &j);
    mmp ret = getout(1, 1, n, i, j);
    printf("%d\n", (ret.a[0][4] < n ? ret.a[0][4] : -1));
  }
  return 0;
}

```