Let's call the roundness of the number the number of zeros to which it ends.

You have an array of n numbers. You need to choose a subset of exactly k numbers so that the roundness of the product of the selected numbers will be maximum possible.

Input

The first line contains two integer numbers n and k (1 ≤ n ≤ 200, 1 ≤ k ≤ n).

The second line contains n space-separated integer numbers a1, a2, ..., an (1 ≤ ai ≤ 1018).

Output

Print maximal roundness of product of the chosen subset of length k.

Examples

Input

3 2
50 4 20


Output

3


Input

5 3
15 16 3 25 9


Output

3


Input

3 3
9 77 13


Output

0

Note

In the first example there are 3 subsets of 2 numbers. [50, 4] has product 200 with roundness 2, [4, 20] — product 80, roundness 1, [50, 20] — product 1000, roundness 3.

In the second example subset [15, 16, 25] has product 6000, roundness 3.

In the third example all subsets has product with roundness 0.
#include <bits/stdc++.h>
using namespace std;
int dp[205][10050] = {0};
int main() {
  memset(dp, 0x80, sizeof(dp));
  dp[0][0] = 0;
  int n, k;
  scanf("%d%d", &n, &k);
  int s = 0;
  for (int i = 1; i <= n; i++) {
    long long num;
    scanf("%I64d", &num);
    int n2 = 0, n5 = 0;
    for (; !(num % 5); num /= 5) n5++;
    for (; !(num % 2); num /= 2) n2++;
    s += n2;
    for (int j = min(i, k); j >= 1; j--)
      for (int l = s; l >= n2; l--)
        dp[j][l] = max(dp[j][l], dp[j - 1][l - n2] + n5);
  }
  int ans = 0;
  for (int i = 1; i <= s; i++) ans = max(ans, min(i, dp[k][i]));
  printf("%d\n", ans);
  return 0;
}
