#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 100;
const int mod = 1e9 + 7;
const int inf = 1e9;
struct node {
  int dp[5][5];
  node() {
    for (int i = 0; i < 5; i++) {
      for (int j = 0; j < 5; j++) {
        dp[i][j] = inf;
      }
    }
  }
};
int n, m;
node seg[maxn << 2];
string st, f = "2017 ", f2 = "20166";
node merge(node l, node r) {
  node c;
  for (int i = 0; i < 5; i++) {
    for (int j = i; j < 5; j++) {
      for (int k = j; k < 5; k++) {
        c.dp[i][k] = min(c.dp[i][k], l.dp[i][j] + r.dp[j][k]);
      }
    }
  }
  return c;
}
void bld(int id, int s, int e) {
  if (e - s == 1) {
    for (int i = 0; i < 5; i++) {
      if (st[s] == f[i]) {
        seg[id].dp[i][i + 1] = 0;
        seg[id].dp[i][i] = 1;
      } else if (st[s] == f2[i]) {
        seg[id].dp[i][i] = 1;
      } else {
        seg[id].dp[i][i] = 0;
      }
    }
    return;
  }
  int mid = (s + e) >> 1;
  bld((id << 1), s, mid);
  bld(((id << 1) | 1), mid, e);
  seg[id] = merge(seg[(id << 1)], seg[((id << 1) | 1)]);
  return;
}
node get(int id, int s, int e, int l, int r) {
  if (l <= s && e <= r) return seg[id];
  int mid = (s + e) >> 1;
  if (r <= mid) return get((id << 1), s, mid, l, r);
  if (l >= mid) return get(((id << 1) | 1), mid, e, l, r);
  return merge(get((id << 1), s, mid, l, r),
               get(((id << 1) | 1), mid, e, l, r));
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  cin >> n >> m >> st;
  bld(1, 0, n);
  for (int i = 0; i < m; i++) {
    int l, r;
    cin >> l >> r;
    int x = get(1, 0, n, l - 1, r).dp[0][4];
    if (x == inf) x = -1;
    cout << x << "\n";
  }
  return 0;
}

### Prompt

Please create a solution in Cpp 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 + 100;
const int mod = 1e9 + 7;
const int inf = 1e9;
struct node {
  int dp[5][5];
  node() {
    for (int i = 0; i < 5; i++) {
      for (int j = 0; j < 5; j++) {
        dp[i][j] = inf;
      }
    }
  }
};
int n, m;
node seg[maxn << 2];
string st, f = "2017 ", f2 = "20166";
node merge(node l, node r) {
  node c;
  for (int i = 0; i < 5; i++) {
    for (int j = i; j < 5; j++) {
      for (int k = j; k < 5; k++) {
        c.dp[i][k] = min(c.dp[i][k], l.dp[i][j] + r.dp[j][k]);
      }
    }
  }
  return c;
}
void bld(int id, int s, int e) {
  if (e - s == 1) {
    for (int i = 0; i < 5; i++) {
      if (st[s] == f[i]) {
        seg[id].dp[i][i + 1] = 0;
        seg[id].dp[i][i] = 1;
      } else if (st[s] == f2[i]) {
        seg[id].dp[i][i] = 1;
      } else {
        seg[id].dp[i][i] = 0;
      }
    }
    return;
  }
  int mid = (s + e) >> 1;
  bld((id << 1), s, mid);
  bld(((id << 1) | 1), mid, e);
  seg[id] = merge(seg[(id << 1)], seg[((id << 1) | 1)]);
  return;
}
node get(int id, int s, int e, int l, int r) {
  if (l <= s && e <= r) return seg[id];
  int mid = (s + e) >> 1;
  if (r <= mid) return get((id << 1), s, mid, l, r);
  if (l >= mid) return get(((id << 1) | 1), mid, e, l, r);
  return merge(get((id << 1), s, mid, l, r),
               get(((id << 1) | 1), mid, e, l, r));
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  ;
  cin >> n >> m >> st;
  bld(1, 0, n);
  for (int i = 0; i < m; i++) {
    int l, r;
    cin >> l >> r;
    int x = get(1, 0, n, l - 1, r).dp[0][4];
    if (x == inf) x = -1;
    cout << x << "\n";
  }
  return 0;
}

```