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
import fileinput, sys
f = fileinput.input()

[n] = [int(i) for i in f[0].split()]
a = [int(x) for x in str(f[1]).split()]
mn = min(a)
b = map(lambda (i, v): i, filter(lambda (i, v): mn == v, enumerate(a)))
print min([b[i+1] - b[i] for i in xrange(len(b)-1)])
