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
import sys
n = int(input())
nums = [x for x in map(int, input().split())]
mini = min(nums)
dists = []
miniDistance = 10**9 + 1 

for i in range(n):
    if nums[i]==mini:
        dists.append(i)
for i in range(1,len(dists)):
    #print("Compare")
    miniDistance = min(dists[i] - dists[i-1], miniDistance)
#print(dists)
print(miniDistance)

