#include <bits/stdc++.h>
using namespace std;
template <class T>
bool mini(T &a, T b) {
  return a > b ? (a = b, true) : false;
}
template <class T>
bool maxi(T &a, T b) {
  return a < b ? (a = b, true) : false;
}
const int axbit = (1 << 18);
int T[2 * axbit + 1][5][5];
int n, q;
const int oo = 1e8;
void combine(int x, int y, int id) {
  for (int i = 0; i < (int)(5); i++)
    for (int j = (int)(i); j <= (int)(4); j++) {
      T[id][i][j] = oo;
      for (int k = (int)(i); k <= (int)(j); k++)
        mini(T[id][i][j], T[x][i][k] + T[y][k][j]);
    }
}
void get(int l, int r, int lo = 0, int hi = axbit - 1, int id = 1) {
  if (l > hi || lo > r) return;
  if (l <= lo && hi <= r) {
    combine(0, id, axbit * 2);
    for (int i = 0; i < (int)(5); i++)
      for (int j = 0; j < (int)(5); j++) T[0][i][j] = T[axbit * 2][i][j];
    return;
  }
  int mid = (lo + hi) >> 1;
  get(l, r, lo, mid, id << 1);
  get(l, r, mid + 1, hi, id << 1 ^ 1);
}
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.precision(10);
  cout << fixed;
  cin >> n >> q;
  for (int i = 0; i < (int)(n); i++) {
    char c;
    cin >> c;
    int cur = axbit + i;
    for (int i = 0; i < (int)(5); i++)
      for (int j = 0; j < (int)(5); j++)
        if (i != j) T[cur][i][j] = oo;
    if (c == '6')
      T[cur][4][4] = T[cur][3][3] = 1;
    else if (c == '7')
      T[cur][3][3] = 1, T[cur][3][4] = 0;
    else if (c == '1')
      T[cur][2][2] = 1, T[cur][2][3] = 0;
    else if (c == '0')
      T[cur][1][1] = 1, T[cur][1][2] = 0;
    else if (c == '2')
      T[cur][0][0] = 1, T[cur][0][1] = 0;
    else
      T[cur][0][0] = 0;
  }
  for (int i = axbit - 1; i; i--) combine(i << 1, i << 1 ^ 1, i);
  while (q--) {
    int l, r;
    cin >> l >> r;
    l--;
    r--;
    for (int i = 0; i < (int)(5); i++)
      for (int j = 0; j < (int)(5); j++) T[0][i][j] = oo;
    T[0][0][0] = 0;
    get(l, r);
    int res = T[0][0][4];
    cout << (res < oo ? res : -1) << "\n";
  }
}

### Prompt

In Cpp, your task is to solve 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;
template <class T>
bool mini(T &a, T b) {
  return a > b ? (a = b, true) : false;
}
template <class T>
bool maxi(T &a, T b) {
  return a < b ? (a = b, true) : false;
}
const int axbit = (1 << 18);
int T[2 * axbit + 1][5][5];
int n, q;
const int oo = 1e8;
void combine(int x, int y, int id) {
  for (int i = 0; i < (int)(5); i++)
    for (int j = (int)(i); j <= (int)(4); j++) {
      T[id][i][j] = oo;
      for (int k = (int)(i); k <= (int)(j); k++)
        mini(T[id][i][j], T[x][i][k] + T[y][k][j]);
    }
}
void get(int l, int r, int lo = 0, int hi = axbit - 1, int id = 1) {
  if (l > hi || lo > r) return;
  if (l <= lo && hi <= r) {
    combine(0, id, axbit * 2);
    for (int i = 0; i < (int)(5); i++)
      for (int j = 0; j < (int)(5); j++) T[0][i][j] = T[axbit * 2][i][j];
    return;
  }
  int mid = (lo + hi) >> 1;
  get(l, r, lo, mid, id << 1);
  get(l, r, mid + 1, hi, id << 1 ^ 1);
}
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.precision(10);
  cout << fixed;
  cin >> n >> q;
  for (int i = 0; i < (int)(n); i++) {
    char c;
    cin >> c;
    int cur = axbit + i;
    for (int i = 0; i < (int)(5); i++)
      for (int j = 0; j < (int)(5); j++)
        if (i != j) T[cur][i][j] = oo;
    if (c == '6')
      T[cur][4][4] = T[cur][3][3] = 1;
    else if (c == '7')
      T[cur][3][3] = 1, T[cur][3][4] = 0;
    else if (c == '1')
      T[cur][2][2] = 1, T[cur][2][3] = 0;
    else if (c == '0')
      T[cur][1][1] = 1, T[cur][1][2] = 0;
    else if (c == '2')
      T[cur][0][0] = 1, T[cur][0][1] = 0;
    else
      T[cur][0][0] = 0;
  }
  for (int i = axbit - 1; i; i--) combine(i << 1, i << 1 ^ 1, i);
  while (q--) {
    int l, r;
    cin >> l >> r;
    l--;
    r--;
    for (int i = 0; i < (int)(5); i++)
      for (int j = 0; j < (int)(5); j++) T[0][i][j] = oo;
    T[0][0][0] = 0;
    get(l, r);
    int res = T[0][0][4];
    cout << (res < oo ? res : -1) << "\n";
  }
}

```