#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 15;
char an[maxn];
const int INF = 0x3f3f3f3f;
const int msize = 6;
const int f_em = 0;
const int f_2 = 1;
const int f_20 = 2;
const int f_201 = 3;
const int f_2016 = 4;
const int f_2017 = 5;
class matix {
 public:
  int mdata[msize][msize];
  matix(int value = 0) {}
  matix(const matix& s1) {
    for (int j = 0; j < msize; j++)
      for (int i = 0; i < msize; i++) {
        mdata[i][j] = s1.mdata[i][j];
      }
  }
  matix(char sa);
  matix operator*(const matix& s1) const {
    matix ans = 0;
    for (int i = 0; i < msize; i++) {
      for (int j = 0; j < msize; j++) {
        ans.mdata[i][j] = INF;
        for (int k = 0; k < msize; k++) {
          ans.mdata[i][j] = min(mdata[i][k] + s1.mdata[k][j], ans.mdata[i][j]);
        }
      }
    }
    return ans;
  }
  void out() {
    for (int i = 0; i < msize; i++) {
      for (int j = 0; j < msize; j++) {
        cout << mdata[i][j] << ' ';
      }
      cout << endl;
    }
    cout << endl;
  }
};
matix::matix(char s1) {
  memset(mdata, 0x3f, sizeof(mdata));
  for (int i = 0; i < msize; i++) mdata[i][i] = 0;
  if (s1 == '2') {
    mdata[f_em][f_2] = 0;
    mdata[f_em][f_em] = 1;
  } else if (s1 == '0') {
    mdata[f_2][f_20] = 0;
    mdata[f_2][f_2] = 1;
  } else if (s1 == '1') {
    mdata[f_20][f_201] = 0;
    mdata[f_20][f_20] = 1;
  } else if (s1 == '6') {
    mdata[f_201][f_2016] = 0;
    mdata[f_2017][f_2016] = 0;
    mdata[f_2017][f_2017] = 1;
    mdata[f_201][f_201] = 1;
  } else if (s1 == '7') {
    mdata[f_201][f_2017] = 0;
    mdata[f_201][f_201] = 1;
  }
}
matix node[4 * maxn + 15];
void up(int o) { node[o] = node[o << 1] * node[(o << 1) | 1]; }
void built(int l, int r, int o) {
  if (l == r) {
    node[o] = matix(an[l - 1]);
    return;
  }
  int mid = (l + r) >> 1;
  built(l, mid, o << 1);
  built(mid + 1, r, (o << 1) | 1);
  up(o);
}
matix query(int a, int b, int l, int r, int o) {
  if (a <= l && r <= b) {
    return node[o];
  }
  int mid = (l + r) >> 1;
  matix ans('c');
  if (a <= mid) {
    ans = ans * query(a, b, l, mid, o << 1);
  }
  if (b > mid) {
    ans = ans * query(a, b, mid + 1, r, (o << 1) | 1);
  }
  return ans;
}
int main() {
  int n, q;
  while (cin >> n >> q) {
    scanf("%s", an);
    built(1, n, 1);
    int a, b;
    while (q--) {
      scanf("%d%d", &a, &b);
      matix ansm = query(a, b, 1, n, 1);
      int ans = ansm.mdata[f_em][f_2017];
      if (ans >= INF) {
        printf("-1\n");
      } else {
        printf("%d\n", ans);
      }
    }
  }
  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 + 15;
char an[maxn];
const int INF = 0x3f3f3f3f;
const int msize = 6;
const int f_em = 0;
const int f_2 = 1;
const int f_20 = 2;
const int f_201 = 3;
const int f_2016 = 4;
const int f_2017 = 5;
class matix {
 public:
  int mdata[msize][msize];
  matix(int value = 0) {}
  matix(const matix& s1) {
    for (int j = 0; j < msize; j++)
      for (int i = 0; i < msize; i++) {
        mdata[i][j] = s1.mdata[i][j];
      }
  }
  matix(char sa);
  matix operator*(const matix& s1) const {
    matix ans = 0;
    for (int i = 0; i < msize; i++) {
      for (int j = 0; j < msize; j++) {
        ans.mdata[i][j] = INF;
        for (int k = 0; k < msize; k++) {
          ans.mdata[i][j] = min(mdata[i][k] + s1.mdata[k][j], ans.mdata[i][j]);
        }
      }
    }
    return ans;
  }
  void out() {
    for (int i = 0; i < msize; i++) {
      for (int j = 0; j < msize; j++) {
        cout << mdata[i][j] << ' ';
      }
      cout << endl;
    }
    cout << endl;
  }
};
matix::matix(char s1) {
  memset(mdata, 0x3f, sizeof(mdata));
  for (int i = 0; i < msize; i++) mdata[i][i] = 0;
  if (s1 == '2') {
    mdata[f_em][f_2] = 0;
    mdata[f_em][f_em] = 1;
  } else if (s1 == '0') {
    mdata[f_2][f_20] = 0;
    mdata[f_2][f_2] = 1;
  } else if (s1 == '1') {
    mdata[f_20][f_201] = 0;
    mdata[f_20][f_20] = 1;
  } else if (s1 == '6') {
    mdata[f_201][f_2016] = 0;
    mdata[f_2017][f_2016] = 0;
    mdata[f_2017][f_2017] = 1;
    mdata[f_201][f_201] = 1;
  } else if (s1 == '7') {
    mdata[f_201][f_2017] = 0;
    mdata[f_201][f_201] = 1;
  }
}
matix node[4 * maxn + 15];
void up(int o) { node[o] = node[o << 1] * node[(o << 1) | 1]; }
void built(int l, int r, int o) {
  if (l == r) {
    node[o] = matix(an[l - 1]);
    return;
  }
  int mid = (l + r) >> 1;
  built(l, mid, o << 1);
  built(mid + 1, r, (o << 1) | 1);
  up(o);
}
matix query(int a, int b, int l, int r, int o) {
  if (a <= l && r <= b) {
    return node[o];
  }
  int mid = (l + r) >> 1;
  matix ans('c');
  if (a <= mid) {
    ans = ans * query(a, b, l, mid, o << 1);
  }
  if (b > mid) {
    ans = ans * query(a, b, mid + 1, r, (o << 1) | 1);
  }
  return ans;
}
int main() {
  int n, q;
  while (cin >> n >> q) {
    scanf("%s", an);
    built(1, n, 1);
    int a, b;
    while (q--) {
      scanf("%d%d", &a, &b);
      matix ansm = query(a, b, 1, n, 1);
      int ans = ansm.mdata[f_em][f_2017];
      if (ans >= INF) {
        printf("-1\n");
      } else {
        printf("%d\n", ans);
      }
    }
  }
  return 0;
}

```