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
n, l = int(input()), list(map(int, raw_input().split(' ')))
m, k = min(l), list()
for i in enumerate(l):
    if i[1] == m:
        k.append(i[0])
s = k[1] - k[0]
for i in range(1, len(k) - 1):
    if k[i + 1] - k[i] < s:
        s = k[i + 1] - k[i]
print(s)