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 Educational35;

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.OptionalInt;

public class A {
        String INPUT = "8 \n 1 2 3 1 32 1 2 4";

        void solve()
        {
                final int n = i();
                final int[] array = ia(n);
                final int  min = Arrays
                        .stream(array)
                        .min()
                        .getAsInt();
                int ans = Integer.MAX_VALUE;
                int ans1 = -10000000;
                for(int i = 0 ; i<n ; i++)
                {
                        if(array[i] == min)
                        {
                                ans = Math.min(ans,i-ans1);
                                ans1 = i;
                        }
                }
                out.print(ans);

        }
        ///////////////////////////////////////
        void run() throws Exception{
                is = oj ? System.in: new ByteArrayInputStream(INPUT.getBytes());
                //is = System.in;
                out = new PrintWriter(System.out);
                int t = 1;
                while(t-->0)	solve();
                out.flush();
        }
        public static void main(String[] args)throws Exception {
                new A().run();
        }
        InputStream is;
        PrintWriter out;
        private byte[] inbuf = new byte[1024];
        public int lenbuf = 0, ptrbuf = 0;

        private int readByte()
        {
                if(lenbuf == -1)throw new InputMismatchException();
                if(ptrbuf >= lenbuf){
                        ptrbuf = 0;
                        try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
                        if(lenbuf <= 0)return -1;
                }
                return inbuf[ptrbuf++];
        }

        private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
        private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }

        private double d() { return Double.parseDouble(s()); }
        private char c() { return (char)skip(); }

        private String s()
        {
                int b = skip();
                StringBuilder sb = new StringBuilder();
                while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
                        sb.appendCodePoint(b);
                        b = readByte();
                }
                return sb.toString();
        }

        private char[] sa(int n)
        {
                char[] buf = new char[n];
                int b = skip(), p = 0;
                while(p < n && !(isSpaceChar(b))){
                        buf[p++] = (char)b;
                        b = readByte();
                }
                return n == p ? buf : Arrays.copyOf(buf, p);
        }

        private char[][] nm(int n, int m)
        {
                char[][] map = new char[n][];
                for(int i = 0;i < n;i++)map[i] = sa(m);
                return map;
        }

        private int[] ia(int n)
        {
                int[] a = new int[n];
                for(int i = 0;i < n;i++)a[i] = i();
                return a;
        }

        private int i()
        {
                int num = 0, b;
                boolean minus = false;
                while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
                if(b == '-'){
                        minus = true;
                        b = readByte();
                }

                while(true){
                        if(b >= '0' && b <= '9'){
                                num = num * 10 + (b - '0');
                        }else{
                                return minus ? -num : num;
                        }
                        b = readByte();
                }
        }

        private long l()
        {
                long num = 0;
                int b;
                boolean minus = false;
                while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
                if(b == '-'){
                        minus = true;
                        b = readByte();
                }

                while(true){
                        if(b >= '0' && b <= '9'){
                                num = num * 10 + (b - '0');
                        }else{
                                return minus ? -num : num;
                        }
                        b = readByte();
                }
        }

        private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
        private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }

}
