p03922 CODE FESTIVAL 2016 Final (Parallel) - Pair Cards
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
```python
import math

N, M = map(int, input().split())
X = list(map(int, input().split()))
mod_arr = [{} for i in range(M)]
for x in X:
    d = mod_arr[x % M]
    if x in d:
        d[x] += 1
    else:
        d[x] = 1
ans = 0

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

def calc_only_one(d):
    sum_v = sum(d.values())
    return sum_v // 2

ans += calc_only_one(mod_arr[0])
# even pattern
if M % 2 == 0:
    ans += calc_only_one(mod_arr[M // 2])

def calc_two(d_S, d_T):
    res = 0
    if len(d_S) == 0:
        for v in d_T.values():
            res += v // 2
        return res
    elif len(d_T) == 0:
        for v in d_S.values():
            res += v // 2
        return res

    if sum(d_S.values()) < sum(d_T.values()):
        d_S, d_T = d_T, d_S
    cnt_S = sum(d_S.values())
    cnt_T = sum(d_T.values())
    remain_for_pair = cnt_S - cnt_T
    max_pair_cnt = sum([v // 2 for v in d_S.values()])
    pair_cnt = min(remain_for_pair // 2 , max_pair_cnt)
    res = cnt_T + pair_cnt
    # print(d_S, d_T)
    # print(remain_for_pair, max_pair_cnt, pair_cnt, res)
    return res


for i in range(1, math.ceil(M / 2)):
    ans += calc_two(mod_arr[i], mod_arr[M - i])
print(ans)


```