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())
cnt=[0]*(max(x)+1)
for i in xrange(n):
    cnt[x[i]]+=1
samemod=[0]*m
for i in xrange(n):
    samemod[x[i]%m]+=1
ans=0
for i in xrange((m+1)/2):
    if i==0:
        ans+=samemod[0]/2
        samemod[0]=0
    else:
        ans+=min(samemod[i],samemod[m-i])
        if samemod[i]>=samemod[m-i]:
            samemod[i]-=samemod[m-i]
            samemod[m-i]=0
        else:
            samemod[m-i]-=samemod[i]
            samemod[i]=0
if (m+1)%2==1:
    ans+=samemod[(m+1)/2]/2
    samemod[(m+1)/2]=0
mp=[[] for _ in xrange(m)]
for i in xrange(1,max(x)+1):
    mp[i%m].append(cnt[i])
for i in xrange(m):
    mp[i].sort()
    mp[i].reverse()

for i in xrange(m):
    for j in xrange(len(mp[i])):
        if mp[i][j]>=2:
            if samemod[i]>=mp[i][j]:
                ans+=mp[i][j]/2
                if mp[i][j]%2==0:
                    samemod[i]-=mp[i][j]
                else:
                    samemod[i]-=mp[i][j]-1
            else:
                ans+=samemod[i]/2
                samemod[i]=0
        else:
            break
print(ans)
