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
# -*- coding: utf-8 -*-
import sys,copy,math,heapq,itertools as it,fractions,re,bisect,collections as coll

N, M = map(int, raw_input().split())
X = map(int, raw_input().split())

cnt = [0]*100005
for x in X:
    cnt[x] += 1

pair = [0]*M
for i in xrange(100005):
    pair[i%M] += cnt[i]/2
    cnt[i] %= 2

mod = [0]*M
for i in xrange(100005):
    mod[i%M] += cnt[i]

ans = sum(pair)
for i in xrange(M):
    if i == 0 or i == M - i:
        ans += mod[i]/2 
        mod[i] %= 2
    else:
        m = min(mod[i], mod[M - i])
        ans += m
        mod[i] -= m
        mod[M - i] -= m

for i in xrange(1, M):
    while pair[i] >= 1 and mod[M - i] >= 2:
        ans += 1
        pair[i] -= 1
        mod[M - i] -= 2


print ans
