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
max=min
n = int(input())
a = [int(x) for x in input().split()]
a = [100000000000] + a + [1000000000000]

f = max(a)
indi = []
for i in range(1,n+1):
    if a[i]<=a[i+1] and a[i] <= a[i-1] and a[i]==f:
        indi.append(i)
best = 10000000000000000000
for i in range(len(indi)-1):
    best = max(best,indi[i+1]-indi[i])
print(best)
