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Longest Subarray With Sum Divisible By K

1. You are given an array of integers(arr) and a number K. 2. You have to find length of the longest subarray whose sum is divisible by K.

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Longest Subarray With Sum Divisible By K

easy

1. You are given an array of integers(arr) and a number K. 2. You have to find length of the longest subarray whose sum is divisible by K.

Constraints

1 <= N,K <= 10^5 -1000 <= arr[i] <= 1000

Format

Input

A number N arr1 arr2.. N numbers A number K

Output

A number representing length of the longest subarray whose sum is divisible by K.

Example

Sample Input

6 2 7 6 1 4 5 3

Sample Output

4

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