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 java.io.*;
import java.util.*;

public class Problem911A {
        public static void main(String args[]) throws IOException {
                Scanner sc = new Scanner(System.in);
                int n = sc.nextInt(), dist = 100001, pos = -1;
                int ar[] = new int[n];
                int min = 1000000001;
                
                for(int i = 0; i < n; i++) {
                        ar[i] = sc.nextInt();
                        if(min > ar[i]) {
                                min = ar[i];
                        }
                }
                
                
                for(int i = 0; i < n; i++) {
                        if(min == ar[i]) {
                                pos = i;
                                break;
                        }
                }
                
                for(int i = pos+1; i < n; i++) {
                        if(ar[i] == min) {
                                if(dist > i - pos) {
                                        dist = i - pos;
                                }
                                
                                pos = i;
                        }
                }
                
                System.out.println(dist);
        }
}