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
noe = int(input())
arr = [int(x) for x in input().split()]
sarr= sorted(arr)

need = -1
for i in range(1, noe):
    if sarr[i] == sarr[i-1]:
        need = sarr[i]
        break
need = sarr[i]

indices = sorted([i for i, x in enumerate(arr) if x ==need])

mins = 10e9
for x in range(1, len(indices)):
    mins = min(mins, indices[x] - indices[x-1])
print(mins)