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())
s = input()
a = []
s = s.split()
mn = 1000000001
count = 0
minres = 100000
for c in s:
    if int(c)<mn:
        mn = int(c)
        minres = 100000
        count = 0
    if count!=0 and int(c)==mn:
        if count<minres:
            minres = count
        count=0
    count += 1
print(minres)