#include <bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 10, inf = 1e7;
int n, q;
string s;
struct node {
  int dp[5][5];
  node() { fill_n(dp[0], 5 * 5, inf); }
} seg[4 * maxn];
node zx;
node get(int id, int sl, int sr, int l, int r) {
  int u = max(0, min(r, sr) - max(l, sl));
  if (u == 0) {
    for (int i = 0; i < 5; i++) zx.dp[i][i] = 0;
    return zx;
  }
  if (u == sr - sl) return seg[id];
  int mid = (sr + sl) / 2;
  node a = get(2 * id, sl, mid, l, r);
  node b = get(2 * id + 1, mid, sr, l, r);
  node ans;
  for (int i = 0; i < 5; i++)
    for (int j = i; j < 5; j++)
      for (int k = i; k < 5; k++)
        ans.dp[i][j] = min(ans.dp[i][j], a.dp[i][k] + b.dp[k][j]);
  return ans;
}
void make(int id = 1, int sl = 0, int sr = n) {
  if (sr - sl == 1) {
    for (int i = 0; i < 5; i++) seg[id].dp[i][i] = 0;
    if (s[sl] == '2') {
      seg[id].dp[0][1] = 0;
      seg[id].dp[0][0] = 1;
    } else if (s[sl] == '0') {
      seg[id].dp[1][2] = 0;
      seg[id].dp[1][1] = 1;
    } else if (s[sl] == '1') {
      seg[id].dp[2][3] = 0;
      seg[id].dp[2][2] = 1;
    } else if (s[sl] == '7') {
      seg[id].dp[3][4] = 0;
      seg[id].dp[3][3] = 1;
    } else if (s[sl] == '6') {
      seg[id].dp[3][3] = 1;
      seg[id].dp[4][4] = 1;
    }
    return;
  }
  int mid = (sl + sr) / 2;
  make(2 * id, sl, mid);
  make(2 * id + 1, mid, sr);
  for (int i = 0; i < 5; i++)
    for (int j = i; j < 5; j++)
      for (int k = i; k < 5; k++)
        seg[id].dp[i][j] = min(seg[id].dp[i][j],
                               seg[2 * id].dp[i][k] + seg[2 * id + 1].dp[k][j]);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> q;
  cin >> s;
  make();
  for (int i = 0; i < q; i++) {
    int l, r;
    cin >> l >> r;
    l--;
    node ki = get(1, 0, n, l, r);
    if (ki.dp[0][4] == inf)
      cout << -1 << endl;
    else
      cout << ki.dp[0][4] << endl;
  }
}

### 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 + 10, inf = 1e7;
int n, q;
string s;
struct node {
  int dp[5][5];
  node() { fill_n(dp[0], 5 * 5, inf); }
} seg[4 * maxn];
node zx;
node get(int id, int sl, int sr, int l, int r) {
  int u = max(0, min(r, sr) - max(l, sl));
  if (u == 0) {
    for (int i = 0; i < 5; i++) zx.dp[i][i] = 0;
    return zx;
  }
  if (u == sr - sl) return seg[id];
  int mid = (sr + sl) / 2;
  node a = get(2 * id, sl, mid, l, r);
  node b = get(2 * id + 1, mid, sr, l, r);
  node ans;
  for (int i = 0; i < 5; i++)
    for (int j = i; j < 5; j++)
      for (int k = i; k < 5; k++)
        ans.dp[i][j] = min(ans.dp[i][j], a.dp[i][k] + b.dp[k][j]);
  return ans;
}
void make(int id = 1, int sl = 0, int sr = n) {
  if (sr - sl == 1) {
    for (int i = 0; i < 5; i++) seg[id].dp[i][i] = 0;
    if (s[sl] == '2') {
      seg[id].dp[0][1] = 0;
      seg[id].dp[0][0] = 1;
    } else if (s[sl] == '0') {
      seg[id].dp[1][2] = 0;
      seg[id].dp[1][1] = 1;
    } else if (s[sl] == '1') {
      seg[id].dp[2][3] = 0;
      seg[id].dp[2][2] = 1;
    } else if (s[sl] == '7') {
      seg[id].dp[3][4] = 0;
      seg[id].dp[3][3] = 1;
    } else if (s[sl] == '6') {
      seg[id].dp[3][3] = 1;
      seg[id].dp[4][4] = 1;
    }
    return;
  }
  int mid = (sl + sr) / 2;
  make(2 * id, sl, mid);
  make(2 * id + 1, mid, sr);
  for (int i = 0; i < 5; i++)
    for (int j = i; j < 5; j++)
      for (int k = i; k < 5; k++)
        seg[id].dp[i][j] = min(seg[id].dp[i][j],
                               seg[2 * id].dp[i][k] + seg[2 * id + 1].dp[k][j]);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> q;
  cin >> s;
  make();
  for (int i = 0; i < q; i++) {
    int l, r;
    cin >> l >> r;
    l--;
    node ki = get(1, 0, n, l, r);
    if (ki.dp[0][4] == inf)
      cout << -1 << endl;
    else
      cout << ki.dp[0][4] << endl;
  }
}

```