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 = map(int, input())

from collections import defaultdict

m = defaultdict(list)
arr = map(int, input().split(' '))
_min = None
i = 0
for elem in arr:
    if _min == None: _min = elem
    _min = min(_min, elem)
    m[elem].append(i)
    i += 1

positions = m[_min]
l = sorted(positions)
minDiff = l[1] - l[0]

for i in range(2, len(l)):
    minDiff = min(minDiff, l[i] - l[i - 1])

print(minDiff)
