#include <bits/stdc++.h>
using namespace std;
const int INF = 1e7 + 5;
const int MAXN = 2e5 + 5;
string s = "";
int n = 0, q = 0;
struct M {
  int m[5][5];
};
M t[4 * MAXN];
M mNeutral, mTwo, mZero, mOne, mSeven, mSix;
void initMatrices() {
  for (int i = 0; i < 5; i++)
    for (int j = 0; j < 5; j++) {
      mNeutral.m[i][j] = INF;
      mTwo.m[i][j] = INF;
      mZero.m[i][j] = INF;
      mOne.m[i][j] = INF;
      mSeven.m[i][j] = INF;
      mSix.m[i][j] = INF;
    }
  for (int i = 0; i < 5; i++) {
    mNeutral.m[i][i] = 0;
    mTwo.m[i][i] = 0;
    mZero.m[i][i] = 0;
    mOne.m[i][i] = 0;
    mSeven.m[i][i] = 0;
    mSix.m[i][i] = 0;
  }
  mTwo.m[0][0] = 1;
  mTwo.m[0][1] = 0;
  mZero.m[1][1] = 1;
  mZero.m[1][2] = 0;
  mOne.m[2][2] = 1;
  mOne.m[2][3] = 0;
  mSeven.m[3][3] = 1;
  mSeven.m[3][4] = 0;
  mSix.m[3][3] = 1;
  mSix.m[4][4] = 1;
}
M plusMatrices(M a, M b) {
  M result;
  for (int i = 0; i < 5; i++)
    for (int j = 0; j < 5; j++) result.m[i][j] = INF;
  for (int i = 0; i < 5; i++)
    for (int j = i; j < 5; j++)
      for (int k = i; k <= j; k++)
        if (a.m[i][k] < INF && b.m[k][j] < INF)
          result.m[i][j] = min(result.m[i][j], a.m[i][k] + b.m[k][j]);
  return result;
}
void build(int v, int tl, int tr) {
  if (tl == tr) {
    switch (s[tl]) {
      case '0':
        t[v] = mZero;
        break;
      case '1':
        t[v] = mOne;
        break;
      case '2':
        t[v] = mTwo;
        break;
      case '7':
        t[v] = mSeven;
        break;
      case '6':
        t[v] = mSix;
        break;
      default:
        t[v] = mNeutral;
        break;
    }
    return;
  }
  int tm = (tl + tr) >> 1;
  build(2 * v + 1, tl, tm);
  build(2 * v + 2, tm + 1, tr);
  t[v] = plusMatrices(t[2 * v + 1], t[2 * v + 2]);
  return;
}
M findResult(int v, int tl, int tr, int l, int r) {
  if (l > r) return mNeutral;
  if (tl == l && tr == r) return t[v];
  int tm = (tl + tr) >> 1;
  return plusMatrices(findResult(2 * v + 1, tl, tm, l, min(tm, r)),
                      findResult(2 * v + 2, tm + 1, tr, max(tm + 1, l), r));
}
int main() {
  initMatrices();
  cin >> n >> q;
  cin >> s;
  build(0, 0, n - 1);
  for (int i = 0; i < q; i++) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    M result = findResult(0, 0, n - 1, a, b);
    if (result.m[0][4] != INF)
      cout << result.m[0][4] << endl;
    else
      cout << "-1\n";
  }
  return 0;
}

### Prompt

Please provide a CPP coded solution 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 int INF = 1e7 + 5;
const int MAXN = 2e5 + 5;
string s = "";
int n = 0, q = 0;
struct M {
  int m[5][5];
};
M t[4 * MAXN];
M mNeutral, mTwo, mZero, mOne, mSeven, mSix;
void initMatrices() {
  for (int i = 0; i < 5; i++)
    for (int j = 0; j < 5; j++) {
      mNeutral.m[i][j] = INF;
      mTwo.m[i][j] = INF;
      mZero.m[i][j] = INF;
      mOne.m[i][j] = INF;
      mSeven.m[i][j] = INF;
      mSix.m[i][j] = INF;
    }
  for (int i = 0; i < 5; i++) {
    mNeutral.m[i][i] = 0;
    mTwo.m[i][i] = 0;
    mZero.m[i][i] = 0;
    mOne.m[i][i] = 0;
    mSeven.m[i][i] = 0;
    mSix.m[i][i] = 0;
  }
  mTwo.m[0][0] = 1;
  mTwo.m[0][1] = 0;
  mZero.m[1][1] = 1;
  mZero.m[1][2] = 0;
  mOne.m[2][2] = 1;
  mOne.m[2][3] = 0;
  mSeven.m[3][3] = 1;
  mSeven.m[3][4] = 0;
  mSix.m[3][3] = 1;
  mSix.m[4][4] = 1;
}
M plusMatrices(M a, M b) {
  M result;
  for (int i = 0; i < 5; i++)
    for (int j = 0; j < 5; j++) result.m[i][j] = INF;
  for (int i = 0; i < 5; i++)
    for (int j = i; j < 5; j++)
      for (int k = i; k <= j; k++)
        if (a.m[i][k] < INF && b.m[k][j] < INF)
          result.m[i][j] = min(result.m[i][j], a.m[i][k] + b.m[k][j]);
  return result;
}
void build(int v, int tl, int tr) {
  if (tl == tr) {
    switch (s[tl]) {
      case '0':
        t[v] = mZero;
        break;
      case '1':
        t[v] = mOne;
        break;
      case '2':
        t[v] = mTwo;
        break;
      case '7':
        t[v] = mSeven;
        break;
      case '6':
        t[v] = mSix;
        break;
      default:
        t[v] = mNeutral;
        break;
    }
    return;
  }
  int tm = (tl + tr) >> 1;
  build(2 * v + 1, tl, tm);
  build(2 * v + 2, tm + 1, tr);
  t[v] = plusMatrices(t[2 * v + 1], t[2 * v + 2]);
  return;
}
M findResult(int v, int tl, int tr, int l, int r) {
  if (l > r) return mNeutral;
  if (tl == l && tr == r) return t[v];
  int tm = (tl + tr) >> 1;
  return plusMatrices(findResult(2 * v + 1, tl, tm, l, min(tm, r)),
                      findResult(2 * v + 2, tm + 1, tr, max(tm + 1, l), r));
}
int main() {
  initMatrices();
  cin >> n >> q;
  cin >> s;
  build(0, 0, n - 1);
  for (int i = 0; i < q; i++) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    M result = findResult(0, 0, n - 1, a, b);
    if (result.m[0][4] != INF)
      cout << result.m[0][4] << endl;
    else
      cout << "-1\n";
  }
  return 0;
}

```