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(raw_input())
l = map(int, raw_input().split())
s = set(l)
d = {i:[] for i in s}
for i in range(n):
    d[l[i]].append(i)
mi  = min(l)
k = d[mi]
k.sort()
a = 1000000001
for i in range(len(k)-1):
    if k[i+1] - k[i] < a:
        a = k[i+1] - k[i]
print a

