The student council is preparing for the relay race at the sports festival.

The council consists of n members. They will run one after the other in the race, the speed of member i is s_i. The discrepancy d_i of the i-th stage is the difference between the maximum and the minimum running speed among the first i members who ran. Formally, if a_i denotes the speed of the i-th member who participated in the race, then d_i = max(a_1, a_2, ..., a_i) - min(a_1, a_2, ..., a_i).

You want to minimize the sum of the discrepancies d_1 + d_2 + ... + d_n. To do this, you are allowed to change the order in which the members run. What is the minimum possible sum that can be achieved?

Input

The first line contains a single integer n (1 ≤ n ≤ 2000) — the number of members of the student council.

The second line contains n integers s_1, s_2, ..., s_n (1 ≤ s_i ≤ 10^9) – the running speeds of the members.

Output

Print a single integer — the minimum possible value of d_1 + d_2 + ... + d_n after choosing the order of the members.

Examples

Input


3
3 1 2


Output


3


Input


1
5


Output


0


Input


6
1 6 3 3 6 3


Output


11


Input


6
104 943872923 6589 889921234 1000000000 69


Output


2833800505

Note

In the first test case, we may choose to make the third member run first, followed by the first member, and finally the second. Thus a_1 = 2, a_2 = 3, and a_3 = 1. We have:

  * d_1 = max(2) - min(2) = 2 - 2 = 0. 
  * d_2 = max(2, 3) - min(2, 3) = 3 - 2 = 1. 
  * d_3 = max(2, 3, 1) - min(2, 3, 1) = 3 - 1 = 2. 



The resulting sum is d_1 + d_2 + d_3 = 0 + 1 + 2 = 3. It can be shown that it is impossible to achieve a smaller value.

In the second test case, the only possible rearrangement gives d_1 = 0, so the minimum possible result is 0.
/* package codechef; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{   static long dp[][];
	public static void main (String[] args) throws java.lang.Exception
	{  FastReader in = new FastReader(System.in);
        int t=1;
        //t=in.nextInt();
        while(t>0){
            --t;
            int n = in.nextInt();
            long arr[] = new long[n];
            for(int i = 0;i<n;i++)
            arr[i] = in.nextInt();
            if(n == 1){
            System.out.println(0);
            continue;
            }
            Arrays.sort(arr);
            dp = new long[n+1][n+1];
            for(int i = 0;i<n;i++)
             Arrays.fill(dp[i],-1);
            long ans = findans(arr,0,n-1);
            System.out.println(ans);
        }
	   
	}
	static long findans(long arr[], int s , int e)
	{
	    if(s == e-1)
	    return arr[e] - arr[s];
	    if(dp[s][e]!=-1)
	    return dp[s][e];
	    return dp[s][e] = (arr[e]-arr[s]) + Math.min(findans(arr,s+1,e),findans(arr,s,e-1));
	}
    static int upper_bound(int arr[],int x){
	    int a=Arrays.binarySearch(arr,x);
	    if(a<0){
	        a*=(-1);
	    
	        return a-1; 
	    }
	    else{
	        
	        while(a<arr.length && arr[a]==x)
	           ++a;
	           return a;
	    }
	}
	static long gcd(long a ,long b)
	{
    if(a==0)
    return b;
    else return gcd(b%a,a);
    }
    
//------making a Fendwick tree ---//
	// creating a fendwick tree
	static long ftree[];
	static void buildFendwicktree(int arr[],int n)
	{
		ftree=new long[n+1];
		for(int i=0;i<n;i++)
			upftree(arr[i],i,n);
	}
	static void upftree(int value,int n,int i)
	{
		int index=i+1;
		while(index<=n)
		{
		  ftree[index]+=value;
		  index+=(index&(-index));  // adding last bit to the index 
		}
	}
	static long getSum(int index)
	{
		long sum=0;
		index+=1;
		while(index>0)
		{
			sum+=ftree[index];
			index-=(index&(-index)); // fliping last index of the tree; 
		}
		return sum;
	}
//------Fendwick tree ends ---------//
}


class sgmtree{
    int arr[];
    sgmtree(int input[],int n){
        arr=new int[100001];
        buildtree(input,1,0,n-1);
    }
    void buildtree(int input[],int si,int ss,int se){
        if(ss==se){
         arr[si]=input[ss];
         return;
        }
         int mid=(ss+se)/2;
         buildtree(input,2*si,ss,mid);
         buildtree(input,2*si+1,mid+1,se);
         arr[si]=Math.min(arr[2*si],arr[2*si+1]);
         
    }
    int query(int si,int ss,int se,int qs,int qe){
        if(qs>se  || qe<ss)
         return Integer.MAX_VALUE;
        
        if(ss>=qs && qe>=se)
        return arr[si];
        
        int mid=(ss+se)/2;
        int l=query(2*si,ss,mid,qs,qe);
        int r=query(2*si+1,mid+1,se,qs,qe);
        return Math.min(l,r);
    }
    void update(int input[],int index,int value){
        input[index]=value;
        updateutils(input,1,0,input.length-1,index);
    }
    void updateutils(int input[],int si,int ss,int se,int qi){
        if(ss==se){
            arr[si]=input[ss];
            return;
        }
        int mid=(ss+se)/2;
        if(qi<=mid)
        updateutils(input,2*si,ss,mid,qi);
        else
        updateutils(input,2*si+1,mid+1,se,qi);
        arr[si]=Math.min(arr[2*si],arr[2*si+1]);
    }
    
}
	
	/* This is for sorting first accorting to gain[1] if gain[1] is same the gain[0]
Arrays.sort(gain, (long[] l1, long[] l2) -> {
	        if(l1[1] != l2[1])return Long.compare(l2[1], l1[1]);//Sorting in non-increasing order of gain
	        return Long.compare(l1[0], l2[0]);//Choosing smallest bit among all bits having same gain
	    });
*/

class pair{
    int x,y;
    pair(int x,int y){
        this.x=x;
        this.y=y;
    }
}	
class CompareValue { 
  
    static void compare(pair arr[], int n) 
    { 
        Arrays.sort(arr, new Comparator<pair>() { 
        public int compare(pair p1, pair p2) 
            { 
                return p1.y - p2.y; 
            } 
        }); 
    } 
}
class CompareKey{
    static void compare(pair arr[],int n){
        Arrays.sort(arr,new Comparator<pair>(){
            public int compare(pair p1,pair p2)
            {
                return p2.x-p1.x;
            }
        });
    }
}
class FastReader {

    byte[] buf = new byte[2048];
    int index, total;
    InputStream in;

    FastReader(InputStream is) {
        in = is;
    }

    int scan() throws IOException {
        if (index >= total) {
            index = 0;
            total = in.read(buf);
            if (total <= 0) {
                return -1;
            }
        }
        return buf[index++];
    }

    String next() throws IOException {
        int c;
        for (c = scan(); c <= 32; c = scan()) ;
        StringBuilder sb = new StringBuilder();
        for (; c > 32; c = scan()) {
            sb.append((char) c);
        }
        return sb.toString();
    }

    String nextLine() throws IOException {
        int c;
        for (c = scan(); c <= 32; c = scan()) ;
        StringBuilder sb = new StringBuilder();
        for (; c != 10 && c != 13; c = scan()) {
            sb.append((char) c);
        }
        return sb.toString();
    }

    char nextChar() throws IOException {
        int c;
        for (c = scan(); c <= 32; c = scan()) ;
        return (char) c;
    }

    int nextInt() throws IOException {
        int c, val = 0;
        for (c = scan(); c <= 32; c = scan()) ;
        boolean neg = c == '-';
        if (c == '-' || c == '+') {
            c = scan();
        }
        for (; c >= '0' && c <= '9'; c = scan()) {
            val = (val << 3) + (val << 1) + (c & 15);
        }
        return neg ? -val : val;
    }

    long nextLong() throws IOException {
        int c;
        long val = 0;
        for (c = scan(); c <= 32; c = scan()) ;
        boolean neg = c == '-';
        if (c == '-' || c == '+') {
            c = scan();
        }
        for (; c >= '0' && c <= '9'; c = scan()) {
            val = (val << 3) + (val << 1) + (c & 15);
        }
        return neg ? -val : val;
    }
}	