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 = int(input())
a = [int(i) for i in input().split()]
m = min(a)
m_l = 1
l = []
f = 0
for i in range(n):
    if f:
        if m == a[i]:
            l.append(m_l)
            m_l = 1
        elif f:
            m_l += 1
    else:
        if m == a[i]:
            f = 1
print(min(l))