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Problem Statement

CCOIE is running on a circular runway with length \(n\text{ m}\) clockwisely. His speed is \(1\text{ m/s}\). There are some gems on the ground, dimming by \(1\) unit per second. Of course, if the gems' brightness here is already zero, there is no need to change. At first, the gem brightness of \(1\text{ m}\) from the starting point (clockwise) is \(g_i\). If the gem is \(0\) where he is, or \(0\) at that instant, he begins to rest.

Question: When he finished, how many meters is he from the starting point (counterclockwise) ?

Tips: The answer is a number in the \(0\sim(n-1)\) range.

Input Description

The first line, a number \(n\) (\(n\leq10^5\)). The second line, \(n\) numbers, the \(i+1^{\text{th}}\) one is \(g_i\) (\(g_i\leq10^9\)).

Output Description

You just need to print out a number to represent the answer.

Sample

Input

4
2 3 2 0

Output

2

Big-Data Example

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