Zero Remainder Sum

[vinayaksh42]

Time limit per test1 second Memory limit per test 256 megabytes

You are given a matrix a of size n×m consisting of integers.

You can choose no more than ⌊m2⌋ elements in each row. Your task is to choose these elements in such a way that their sum is divisible by k and this sum is the maximum.

In other words, you can choose no more than a half (rounded down) of elements in each row, you have to find the maximum sum of these elements divisible by k.

Note that you can choose zero elements (and the sum of such set is 0).

Input
The first line of the input contains three integers n, m and k (1≤n,m,k≤70) — the number of rows in the matrix, the number of columns in the matrix and the value of k. The next n lines contain m elements each, where the j-th element of the i-th row is ai,j (1≤ai,j≤70).

Output
Print one integer — the maximum sum divisible by k you can obtain.

Examples
input
3 4 3
1 2 3 4
5 2 2 2
7 1 1 4
output
24
input
5 5 4
1 2 4 2 1
3 5 1 2 4
1 5 7 1 2
3 8 7 1 2
8 4 7 1 6
output
56

Note
In the first example, the optimal answer is 2 and 4 in the first row, 5 and 2 in the second row and 7 and 4 in the third row. The total sum is 2+4+5+2+7+4=24.