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
out = stop = int(input())
input = input().split(' ')
input = list(map(int, input))

strt = 0
minx = min(input)
i_minx1 = input.index(minx)

for i in range(input.count(minx) - 1):
    strt = i_minx1 + 1
    i_minx2 = input.index(minx, strt, stop)
    if i_minx2 - i_minx1 < out:
        out = i_minx2 - i_minx1
    i_minx1 = i_minx2
    
print(out)