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
from collections import Counter

N, M = map(int, input().split())
Xs = list(map(int, input().split()))

cnt = Counter(Xs)

nums = [0] * M
numSames = [0] * M
for key, num in cnt.items():
    k = key%M
    nums[k] += num
    numSames[k] += num//2

ans = 0
for k in range(M//2+1):
    k2 = M-k
    if k == 0 or k == k2:
        numPair = nums[k]//2
        ans += numPair
        nums[k] -= numPair*2
    else:
        numPair = min(nums[k], nums[k2])
        ans += numPair
        nums[k] -= numPair
        nums[k2] -= numPair

for k in range(M):
    ans += min(numSames[k], nums[k]//2)

print(ans)
