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
n,m=map(int,raw_input().split())
x=map(int,raw_input().split())
d={}
for i in xrange(m):
    d[i] = []
for i in xrange(n):
    d[x[i]%m].append(x[i])
c=0
c+=len(d[0])/2
if m%2==0:
    c+=len(d[m/2])/2
for i in xrange(1,(m-1)/2+1):
    a=d[i]
    b=d[m-i]
    if len(a)==len(b):
        c+=len(a)
    elif len(a)<len(b):
        b=sorted(b)
        tmp=0
        i=0
        while i<len(b)-1:
            if b[i] == b[i+1] and len(a)<=len(b)-(tmp+1)*2:
                tmp+=1
                i+=1
            i+=1
        c+=tmp+len(a)
    else:
        a=sorted(a)
        tmp=0
        i=0
        while i<len(a)-1:
            if a[i] == a[i+1] and len(b)<=len(a)-(tmp+1)*2:
                tmp+=1
                i+=1
            i+=1
        c+=tmp+len(b)

print c