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
def arr_enu():
    return [[i, int(x)] for i, x in enumerate(stdin.readline().split())]


from sys import stdin

n, a = int(input()), sorted(arr_enu(), key=lambda x: x[1])
mi, ans = a[0][1], float('inf')
for i in range(1, n):
    if a[i][1] == mi:
        ans = min(ans, a[i][0] - a[i - 1][0])
    else:
        break
print(ans)
