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
class CodeforcesTask911ASolution:
    def __init__(self):
        self.result = ''
        self.n = 0
        self.array = []

    def read_input(self):
        self.n = int(input())
        self.array = [int(x) for x in input().split(" ")]

    def process_task(self):
        mn = min(self.array)
        ind = [x for x in range(self.n) if self.array[x] == mn]
        dists = []
        for x in range(len(ind) - 1):
            dists.append(ind[x + 1] - ind[x])
        self.result = str(min(dists))

    def get_result(self):
        return self.result


if __name__ == "__main__":
    Solution = CodeforcesTask911ASolution()
    Solution.read_input()
    Solution.process_task()
    print(Solution.get_result())
