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 = [None] * n
index_min = [None]
sum = 9999999999
a = list(map(int,input().split()))
#print(a)
index_min[0] = a.index(min(a))
for i in range(index_min[0]):
    if a[index_min[0]] == a[i]:
        index_min.append(i)
for i in range(index_min[0]+1,n):
    if a[index_min[0]] == a[i]:
        index_min.append(i)
#print(index_min)
for i in range(len(index_min)-1):
    #print( index_min[i], index_min[i+1])
    if sum > index_min[i+1] - index_min[i]:
        sum = index_min[i+1] - index_min[i]
    
print(sum)    