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
from sys import stdin
n = int(stdin.readline())
a = map(int,stdin.readline().split())
di = {}
ans = n+5
y = min(a)
for i in xrange(n):
    x = a[i]
    if y== x and x in di:
        ans = min(ans, i - di[x])
    di[x] = i
print ans   