Divisible interval#11342

Divisible interval

1 second
128 megabytes
Medium

You are given an array of integers a_1, a_2, \ldots, a_n. Find any subarray of this array whose sum of elements is exactly divisible by . That is, find numbers (1 \le i \le j \le n) such that the sum (a_i + a_{i+1} + \ldots + a_j) is exactly divisible by . If such a pair cannot be found, then output the pair as an answer.

Input

The first line contains the number (1 \le n \le 10^5) of elements of array . The next line contains integers a_1, a_2, \ldots, a_n (0 \le a_i \le 10^9).

Output

Print any pair (1 \le i \le j \le n) satisfying the condition in one line, or if there is no such pair.

Examples

Example 1

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Note

a_1 + a_2 + a_3 = 4 + 2 + 4 = 10. The sum is divisible by .