#include <bits/stdc++.h>
using namespace std;
const long long mod = 1e9 + 7;
int n, q;
char s[200005];
struct node {
  int dp[5][5];
  node() {
    for (int i = 0; i < 5; i++)
      for (int j = 0; j < 5; j++) dp[i][j] = 1e8;
  }
  void merge_(node nl, node nr) {
    for (int i = 0; i < 5; i++)
      for (int j = i; j < 5; j++)
        for (int k = i; k <= j; k++)
          dp[i][j] = min(dp[i][j], nl.dp[i][k] + nr.dp[k][j]);
    return;
  }
} seg[800005];
void buildTree(int idx, int l, int r) {
  if (l == r) {
    for (int i = 0; i < 5; i++) seg[idx].dp[i][i] = 0;
    int c = s[l - 1] - '0', id = -1;
    if (c == 6)
      seg[idx].dp[3][3] = seg[idx].dp[4][4] = 1;
    else if (c == 7)
      seg[idx].dp[3][4] = 0;
    else if (c == 2)
      id = 0;
    else if (c == 0)
      id = 1;
    else if (c == 1)
      id = 2;
    if (id != -1) {
      seg[idx].dp[id][id] = 1;
      seg[idx].dp[id][id + 1] = 0;
    }
    return;
  }
  buildTree(2 * idx, l, (l + r >> 1));
  buildTree(2 * idx + 1, (l + r >> 1) + 1, r);
  seg[idx].merge_(seg[2 * idx], seg[2 * idx + 1]);
  return;
}
node query(int idx, int l, int r, int &frm, int &to) {
  node ret;
  if (l > to || r < frm) {
    for (int i = 0; i < 5; i++) ret.dp[i][i] = 0;
    return ret;
  }
  if (l >= frm && r <= to) return seg[idx];
  ret.merge_(query(2 * idx, l, (l + r >> 1), frm, to),
             query(2 * idx + 1, (l + r >> 1) + 1, r, frm, to));
  return ret;
}
void solve() {
  cin >> n >> q >> s;
  buildTree(1, 1, n);
  for (int i = 1; i <= q; i++) {
    int a, b;
    cin >> a >> b;
    int ans = query(1, 1, n, a, b).dp[0][4];
    cout << (ans == 1e8 ? -1 : ans) << endl;
  }
  return;
}
int main() {
  solve();
  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 long long mod = 1e9 + 7;
int n, q;
char s[200005];
struct node {
  int dp[5][5];
  node() {
    for (int i = 0; i < 5; i++)
      for (int j = 0; j < 5; j++) dp[i][j] = 1e8;
  }
  void merge_(node nl, node nr) {
    for (int i = 0; i < 5; i++)
      for (int j = i; j < 5; j++)
        for (int k = i; k <= j; k++)
          dp[i][j] = min(dp[i][j], nl.dp[i][k] + nr.dp[k][j]);
    return;
  }
} seg[800005];
void buildTree(int idx, int l, int r) {
  if (l == r) {
    for (int i = 0; i < 5; i++) seg[idx].dp[i][i] = 0;
    int c = s[l - 1] - '0', id = -1;
    if (c == 6)
      seg[idx].dp[3][3] = seg[idx].dp[4][4] = 1;
    else if (c == 7)
      seg[idx].dp[3][4] = 0;
    else if (c == 2)
      id = 0;
    else if (c == 0)
      id = 1;
    else if (c == 1)
      id = 2;
    if (id != -1) {
      seg[idx].dp[id][id] = 1;
      seg[idx].dp[id][id + 1] = 0;
    }
    return;
  }
  buildTree(2 * idx, l, (l + r >> 1));
  buildTree(2 * idx + 1, (l + r >> 1) + 1, r);
  seg[idx].merge_(seg[2 * idx], seg[2 * idx + 1]);
  return;
}
node query(int idx, int l, int r, int &frm, int &to) {
  node ret;
  if (l > to || r < frm) {
    for (int i = 0; i < 5; i++) ret.dp[i][i] = 0;
    return ret;
  }
  if (l >= frm && r <= to) return seg[idx];
  ret.merge_(query(2 * idx, l, (l + r >> 1), frm, to),
             query(2 * idx + 1, (l + r >> 1) + 1, r, frm, to));
  return ret;
}
void solve() {
  cin >> n >> q >> s;
  buildTree(1, 1, n);
  for (int i = 1; i <= q; i++) {
    int a, b;
    cin >> a >> b;
    int ans = query(1, 1, n, a, b).dp[0][4];
    cout << (ans == 1e8 ? -1 : ans) << endl;
  }
  return;
}
int main() {
  solve();
  return 0;
}

```