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
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)

N,M = map(int,input().split())
X = [int(x) for x in input().split()]

counter = [0] * M
pair_counter = [0] * M
se = set()

for x in X:
    r = x%M
    counter[r] += 1
    if x in se:
        pair_counter[r] += 1
        se.remove(x)
    else:
        se.add(x)

answer = 0
for r in range(1,(M+1)//2):
    s = M - r
    cr,cs = counter[r], counter[s]
    pr,ps = pair_counter[r], pair_counter[s]
    if cr < cs:
        cr,cs = cs,cr
        pr,ps = ps,pr
    x = cs + min(pr,(cr-cs)//2)
    answer += x

# 0とM//2
rs = [0] if M&1 else [0,M//2]
answer += sum(counter[r]//2 for r in rs)

print(answer)