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())
src = list(map(int,input().split()))

if M == 1:
    print(N // 2)
    exit()

hist = [0] * M
ctrs = [Counter() for i in range(M)]
for a in src:
    hist[a%M] += 1
    ctrs[a%M].update([a])

ans = 0
for i in range(1, (M+1)//2):
    j = M - i
    if hist[j] < hist[i]: i,j = j,i
    ans += hist[i]
    rem = (hist[j] - hist[i]) // 2
    n = sum([v//2 for v in ctrs[j].values()])
    ans += min(rem, n)

ans += sum(ctrs[0].values()) // 2
if M%2 == 0:
    ans += sum(ctrs[M//2].values()) // 2

print(ans)