#include <bits/stdc++.h>
using namespace std;
int pos[20];
struct nd {
  int a[6][6];
};
nd t[600005];
int n, m;
int sz;
inline void add_node(int x, int y) {
  for (int i = 0; i < 5; ++i)
    for (int j = 0; j < 5; ++j) t[x].a[i][j] = 1e9;
  for (int i = 0; i < 5; ++i) t[x].a[i][i] = 0;
  int z = pos[y];
  if (!z) return;
  if (z == 5) {
    t[x].a[3][3] = 1;
    t[x].a[4][4] = 1;
    return;
  }
  t[x].a[z - 1][z - 1] = 1;
  t[x].a[z - 1][z] = 0;
}
inline nd mrg(nd a, nd b) {
  nd c;
  for (int i = 0; i < 5; ++i) {
    for (int j = i; j < 5; ++j) {
      c.a[i][j] = 1e9;
      for (int k = i; k <= j; ++k)
        c.a[i][j] = min(c.a[i][j], a.a[i][k] + b.a[k][j]);
    }
  }
  return c;
}
nd get(int l, int r, int ll, int rr, int x) {
  if (l >= ll && r <= rr) return t[x];
  int mid = (l + r) >> 1;
  if (rr <= mid)
    return get(l, mid, ll, rr, x + x);
  else if (ll > mid)
    return get(mid + 1, r, ll, rr, x + x + 1);
  else
    return mrg(get(l, mid, ll, rr, x + x), get(mid + 1, r, ll, rr, x + x + 1));
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  pos[0] = 2;
  pos[1] = 3;
  pos[2] = 1;
  pos[7] = 4;
  pos[6] = 5;
  cin >> n >> m;
  string s;
  cin >> s;
  sz = 1;
  while (sz < n) sz += sz;
  for (int i = 0; i < n; ++i) add_node(sz + i, s[i] - '0');
  for (int i = sz - 1; i > 0; --i) {
    t[i] = mrg(t[i + i], t[i + i + 1]);
  }
  for (int i = 1; i <= m; ++i) {
    int x, y;
    cin >> x >> y;
    nd res = get(1, sz, x, y, 1);
    if (res.a[0][4] == 1e9)
      cout << "-1" << '\n';
    else
      cout << res.a[0][4] << '\n';
  }
}

### Prompt

Create a solution in Cpp for 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;
int pos[20];
struct nd {
  int a[6][6];
};
nd t[600005];
int n, m;
int sz;
inline void add_node(int x, int y) {
  for (int i = 0; i < 5; ++i)
    for (int j = 0; j < 5; ++j) t[x].a[i][j] = 1e9;
  for (int i = 0; i < 5; ++i) t[x].a[i][i] = 0;
  int z = pos[y];
  if (!z) return;
  if (z == 5) {
    t[x].a[3][3] = 1;
    t[x].a[4][4] = 1;
    return;
  }
  t[x].a[z - 1][z - 1] = 1;
  t[x].a[z - 1][z] = 0;
}
inline nd mrg(nd a, nd b) {
  nd c;
  for (int i = 0; i < 5; ++i) {
    for (int j = i; j < 5; ++j) {
      c.a[i][j] = 1e9;
      for (int k = i; k <= j; ++k)
        c.a[i][j] = min(c.a[i][j], a.a[i][k] + b.a[k][j]);
    }
  }
  return c;
}
nd get(int l, int r, int ll, int rr, int x) {
  if (l >= ll && r <= rr) return t[x];
  int mid = (l + r) >> 1;
  if (rr <= mid)
    return get(l, mid, ll, rr, x + x);
  else if (ll > mid)
    return get(mid + 1, r, ll, rr, x + x + 1);
  else
    return mrg(get(l, mid, ll, rr, x + x), get(mid + 1, r, ll, rr, x + x + 1));
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  pos[0] = 2;
  pos[1] = 3;
  pos[2] = 1;
  pos[7] = 4;
  pos[6] = 5;
  cin >> n >> m;
  string s;
  cin >> s;
  sz = 1;
  while (sz < n) sz += sz;
  for (int i = 0; i < n; ++i) add_node(sz + i, s[i] - '0');
  for (int i = sz - 1; i > 0; --i) {
    t[i] = mrg(t[i + i], t[i + i + 1]);
  }
  for (int i = 1; i <= m; ++i) {
    int x, y;
    cin >> x >> y;
    nd res = get(1, sz, x, y, 1);
    if (res.a[0][4] == 1e9)
      cout << "-1" << '\n';
    else
      cout << res.a[0][4] << '\n';
  }
}

```