Nearest Minimums

You are given an array of n integer numbers a0, a1, ..., an - 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 ≤ 105) — size of the given array. The second line contains n integers a0, a1, ..., an - 1 (1 ≤ ai ≤ 109) — 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

inputFormat

Input

The first line contains positive integer n (2 ≤ n ≤ 105) — size of the given array. The second line contains n integers a0, a1, ..., an - 1 (1 ≤ ai ≤ 109) — elements of the array. It is guaranteed that in the array a minimum occurs at least two times.

outputFormat

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

样例

2
3 3

1

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