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())
X = list(map(int, input().split()))
S = [0] * M
MM = [0] * M
for x, n in Counter(X).items():
    MM[x%M] += n//2
    S[x%M] += n
ans = 0
ans += S[0] // 2
if M%2 == 0:
    ans += S[M//2] // 2
for i1 in range(1, 1000000):
    i2 = M-i1
    if i1 >= i2:
        break
    s1, s2 = S[i1], S[i2]
    if s1 < s2:
        ans += s1 + min((s2-s1)//2, MM[i2])
    else:
        ans += s2 + min((s1-s2)//2, MM[i1])
print(ans)
