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A. Nearest Minimums

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given an array of *n* integer numbers *a*_{0}, *a*_{1}, ..., *a*_{n - 1}. Find the distance between two closest (nearest) minimums in it. It is guaranteed that in the array a minimum occurs at least two times.

Input

The first line contains positive integer *n* (2 ≤ *n* ≤ 10^{5}) — size of the given array. The second line contains *n* integers *a*_{0}, *a*_{1}, ..., *a*_{n - 1} (1 ≤ *a*_{i} ≤ 10^{9}) — elements of the array. It is guaranteed that in the array a minimum occurs at least two times.

Output

Print the only number — distance between two nearest minimums in the array.

Examples

Input

2

3 3

Output

1

Input

3

5 6 5

Output

2

Input

9

2 1 3 5 4 1 2 3 1

Output

3

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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