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
//package com.nikita;

import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int N = sc.nextInt();
        int[] arr = new int[N];
        int[] arr2 = new int[N];
        int[] arr3 = new int[N];
        int k = 0, j = 0;
        long min = 999999999999l;

        for (int i = 0; i < N; i++) {
            arr[i] = sc.nextInt();
            if (arr[i] < min)
                min = arr[i];
        }

        for (int i = 0; i < N; i++) {
            if (arr[i] == min) {
                arr2[k] = i;
                k++;
            }
        }

        for (int i = 1; i < k; i++) {
            arr3[j] = arr2[i] - arr2[i-1];
            j++;
        }

        min = arr3[0];
        for (int i = 0; i < j; i++) {
            if (arr3[i] < min)
                min = arr3[i];
        }

        System.out.println(min);
    }
}

