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
from collections import defaultdict

MyDict = defaultdict(list)
input()
X = list(map(int, input().split()))
for i in range(len(X)):
    MyDict[X[i]].append(i)
for i in sorted(MyDict.keys()):
    if len(MyDict[i]) > 1:
        Temp = sorted(MyDict[i])
        print(min(Temp[j] - Temp[j - 1] for j in range(1, len(Temp))))
        exit()

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