Takahashi is playing with N cards.

The i-th card has an integer X_i on it.

Takahashi is trying to create as many pairs of cards as possible satisfying one of the following conditions:

* The integers on the two cards are the same.
* The sum of the integers on the two cards is a multiple of M.



Find the maximum number of pairs that can be created.

Note that a card cannot be used in more than one pair.

Constraints

* 2≦N≦10^5
* 1≦M≦10^5
* 1≦X_i≦10^5

Input

The input is given from Standard Input in the following format:


N M
X_1 X_2 ... X_N


Output

Print the maximum number of pairs that can be created.

Examples

Input

7 5
3 1 4 1 5 9 2


Output

3


Input

15 10
1 5 6 10 11 11 11 20 21 25 25 26 99 99 99


Output

6
#include <map>
#include <iostream>
using namespace std;
int main() {
    int n, m; cin >> n >> m;
    int C[100100] = {};
    while (n--) { int x; cin >> x; C[x]++; }
    int sum = 0, ans = 0;
    for (int a = 0; a <= 100000; a += m) sum += C[a];
    ans += sum/2;
    if (m%2==0) {
        sum = 0;
        for (int a = m/2; a <= 100000; a += m) sum += C[a];
        ans += sum/2;
    }
    for (int a = 1, b = m-1; a < b; a++, b--) {
        int c1 = 0, c2 = 0, d1 = 0, d2 = 0;
        for (int x = a; x <= 100000; x += m) { c1 += C[x]%2; d1 += C[x]/2*2; }
        for (int x = b; x <= 100000; x += m) { c2 += C[x]%2; d2 += C[x]/2*2; }
        int c0 = min(c1, c2);
        ans += c0; c1 -= c0; c2 -= c0;
        if (c1 > 0) ans += min(c1, d2), d2 -= min(c1, d2);
        if (c2 > 0) ans += min(c2, d1), d1 -= min(c2, d1);
        ans += d1/2 + d2/2;
    }
    cout << ans << endl;
}
