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.
import java.util.*;
import java.util.Map.Entry;


import java.io.*;
import java.math.*;
import static java.util.stream.Collectors.*;
import static java.util.Map.Entry.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	static long dp[][]=new long[2005][2005];
	public static void main (String[] args) throws IOException
	{
		final long mod=(long) (1e9+7);  
		Reader s=new Reader();
		  PrintWriter pt=new PrintWriter(System.out);
		  
		  BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
//		  int T=s.nextInt();
//		  int T=Integer.parseInt(br.readLine());
		  int T=1;
		  while(T-->0)
		  {
			  int n=s.nextInt();
			  int arr[]=new int[n];
			  
			  for(int i=0;i<n;i++) {
				  arr[i]=s.nextInt();
			  }
			  sort(arr, 0, n-1);
			  for(int i=0;i<dp.length;i++) {
					  Arrays.fill(dp[i], -1);
			  }
			  System.out.println(dpf(arr, 0, n-1));
			  
		  }
		  pt.close();
	}
	
	static long dpf(int arr[], int i, int j) {
		if(dp[i][j]!=-1)
			return dp[i][j];
		if(i==j)
			dp[i][j]= 0;
		else
			dp[i][j]= arr[j]-arr[i]+Math.min(dpf(arr, i+1, j), dpf(arr, i, j-1));
		return dp[i][j];
	}
	
	static int setBit(int S, int j) { return S | 1 << j; }

	static int clearBit(int S, int j) { return S & ~(1 << j); }

	static int toggleBit(int S, int j) { return S ^ 1 << j; }

	static boolean isOn(int S, int j) { return (S & 1 << j) != 0; }

	static int turnOnLastZero(int S) { return S | S + 1; }
	
	static int turnOnLastConsecutiveZeroes(int S) { return S | S - 1; }
	
	static int turnOffLastBit(int S) { return S & S - 1; }
	
	static int turnOffLastConsecutiveBits(int S) { return S & S + 1; }

	static int lowBit(int S) { return S & -S; }

	static int setAll(int N) { return (1 << N) - 1; }

	static int modulo(int S, int N) { return (S & N - 1); }		 //S%N, N is a power of 2

	static boolean isPowerOfTwo(int S) { return (S & S - 1) == 0; }
	
	static boolean isWithin(long x, long y, long d, long k) {
		return x*k*x*k + y*k*y*k <= d*d;
	}
	
	static long modFact(long n, 
            long p) 
	{ 
		if (n >= p) 
		 return 0; 
		
		long result = 1; 
		for (int i = 1; i <= n; i++) 
		 result = (result * i) % p; 
		
		return result; 
	} 
	static int sum(int[] arr, int n)
	{
	    int inc[]=new int[n+1];
	    int dec[]=new int[n+1];
	    inc[0] = arr[0];
	    dec[0] = arr[0];

	    for (int i = 1; i < n; i++) {
	        for (int j = 0; j < i; j++) {
	            if (arr[j] > arr[i]) {
	                dec[i] = max(dec[i], inc[j] + arr[i]);
	            }
	            else if (arr[i] > arr[j]) {
	                inc[i] = max(inc[i], dec[j] + arr[i]);
	            }
	        }
	    }
	    return max(inc[n - 1], dec[n - 1]);
	}
	static long nc2(long a) {
		return a*(a-1)/2;
	}
	public static int numberOfprimeFactors(int n) 
    { 
        // Print the number of 2s that divide n 
		HashSet<Integer> hs = new HashSet<Integer>();
        while (n%2==0) 
        { 
            hs.add(2);
            n /= 2; 
        } 
  
        // n must be odd at this point.  So we can 
        // skip one element (Note i = i +2) 
        for (int i = 3; i <= Math.sqrt(n); i+= 2) 
        { 
            // While i divides n, print i and divide n 
            while (n%i == 0) 
            { 
                hs.add(i);
                n /= i; 
            } 
        } 
  
        // This condition is to handle the case whien 
        // n is a prime number greater than 2 
        if (n > 2) 
            hs.add(n);
        return hs.size();
    } 
	static int gcd(int a, int b) 
    { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    } 




	

	static void reverse(int arr[],int start, int end) 
	{ 
		int temp; 
		   
		while (start < end) 
		{ 
		    temp = arr[start];  
		    arr[start] = arr[end]; 
		    arr[end] = temp; 
		    start++; 
		    end--; 
		}  
	}  
	static void reverse(long arr[],int start, int end) 
	{ 
		long temp; 
		   
		while (start < end) 
		{ 
		    temp = arr[start];  
		    arr[start] = arr[end]; 
		    arr[end] = temp; 
		    start++; 
		    end--; 
		}  
	}  
	static boolean isPrime(int n) 
    { 
        // Corner cases 
        if (n <= 1) return false; 
        if (n <= 3) return true; 
      
        // This is checked so that we can skip  
        // middle five numbers in below loop 
        if (n % 2 == 0 || n % 3 == 0) return false; 
      
        for (int i = 5; i * i <= n; i = i + 6) 
            if (n % i == 0 || n % (i + 2) == 0) 
            return false; 
      
        return true; 
    } 
	static int p2(int n) {
		int k=0;
		while(n>1) {
			if(n%2!=0)
				return k;
			n/=2;
			k++;
		}
		return k;
	}
	static boolean isp2(int n) {
		while(n>1) {
			if(n%2==1)
				return false;
			n/=2;
		}
		return true;
	}
	static int binarySearch(int arr[], int first, int last, int key){  
		   int mid = (first + last)/2;  
		   while( first <= last ){  
		      if ( arr[mid] < key ){  
		        first = mid + 1;     
		      }else if ( arr[mid] == key ){  
		        return mid;  
		      }else{  
		         last = mid - 1;  
		      }  
		      mid = (first + last)/2;  
		   }  
		   return -1;
		 }  

	static void print(int a[][]) {
		for(int i=0;i<a.length;i++)
		{
			for(int j=0;j<a[0].length;j++)
				System.out.print(a[i][j]+" ");
			System.out.println();
		}
	}
	static int max (int x, int y) {
		return (x > y)? x : y;
	} 
	static int search(Pair[] p, Pair pair) {
		int l=0, r=p.length;
		while (l <= r) { 
	        int m = l + (r - l) / 2;
	        if (p[m].compareTo(pair)==0) 
	            return m; 
	        if (p[m].compareTo(pair)<0) 
	            l = m + 1; 
	        else
	            r = m - 1;
	    }
	    return -1;
	}
	static void pa(int a[])
	{
		for(int i=0;i<a.length;i++)
			System.out.print(a[i]+" ");
		System.out.println();
		
	}
	static void pa(long a[])
	{
		for(int i=0;i<a.length;i++)
			System.out.print(a[i]+" ");
		System.out.println();
		
	}
	static void reverseArray(int arr[], 
            int start, int end) 
	{ 
		int temp; 
		   
		while (start < end) 
		{ 
		    temp = arr[start];  
		    arr[start] = arr[end]; 
		    arr[end] = temp; 
		    start++; 
		    end--; 
		}  
	}     
	static boolean isPalindrome(String s) {
		int l=s.length();
		for(int i=0;i<l/2;i++)
		{
			if(s.charAt(i)!=s.charAt(l-i-1))
				return false;
		}
		return true;
	}
	static long nc2(long n, long m) {
		return (n*(n-1)/2)%m;
	}
	static long c(long a) {
		return a*(a+1)/2;
	}
	static int next(int[] arr, int target)  
    {  
        int start = 0, end = arr.length - 1;  
    
        int ans = -1;  
        while (start <= end) {  
            int mid = (start + end) / 2;  
    
            // Move to right side if target is  
            // greater.  
            if (arr[mid] < target) {  
                start = mid + 1;  
            }  
    
            // Move left side.  
            else {  
                ans = mid;  
                end = mid - 1;  
            }  
        }  
        return ans;  
    }  

	static long power(long x, long y, long p) 
    { 
        long res = 1; 
        x = x % p; 
                      
        while (y > 0) 
        { 
            if (y % 2 == 1) 
                res = (res * x) % p; 
            y = y >> 1;
            x = (x * x) % p; 
        } 
        return  res; 
    } 
    static long modInverse(long n, long p) 
    { 
        return power(n, p-2, p); 
    } 
    static long nCrModP(long n, long r, 
                                    long p) 
    { 
        if(r>n)
        	return 0;
    	if (r == 0) 
            return 1; 
        long[] fac = new long[(int) (n+1)]; 
        fac[0] = 1; 
        for (int i = 1 ;i <= n; i++) 
            fac[i] = fac[i-1] * i % p; 
        return (fac[(int) n]* modInverse(fac[(int) r], p) 
                % p * modInverse(fac[(int) (n-r)], p) 
                                    % p) % p; 
    } 
	static String reverse(String str)
	{
		return new StringBuffer(str).reverse().toString();
	}



	static long fastpow(long x, long y, long m)  
    { 
        if (y == 0) 
            return 1; 
          
        long p = fastpow(x, y / 2, m) % m; 
        p = (p * p) % m; 
      
        if (y % 2 == 0) 
            return p; 
        else
            return (x * p) % m; 
    } 
	
	static boolean isPerfectSquare(long l)
	{
		return Math.pow((long)Math.sqrt(l),2)==l;
	}
	
	
	static void merge(long[] arr, int l, int m, int r) 
    { 
        // Find sizes of two subarrays to be merged 
        int n1 = m - l + 1; 
        int n2 = r - m; 
  
        /* Create temp arrays */
        long L[] = new long [n1]; 
        long R[] = new long [n2]; 
  
        /*Copy data to temp arrays*/
        for (int i=0; i<n1; ++i) 
            L[i] = arr[l + i]; 
        for (int j=0; j<n2; ++j) 
            R[j] = arr[m + 1+ j]; 
  
  
        /* Merge the temp arrays */
  
        // Initial indexes of first and second subarrays 
        int i = 0, j = 0; 
  
        // Initial index of merged subarry array 
        int k = l; 
        while (i < n1 && j < n2) 
        { 
            if (L[i] <= R[j]) 
            { 
                arr[k] = L[i]; 
                i++; 
            } 
            else
            { 
                arr[k] = R[j]; 
                j++; 
            } 
            k++; 
        } 
  
        /* Copy remaining elements of L[] if any */
        while (i < n1) 
        { 
            arr[k] = L[i]; 
            i++; 
            k++; 
        } 
  
        /* Copy remaining elements of R[] if any */
        while (j < n2) 
        { 
            arr[k] = R[j]; 
            j++; 
            k++; 
        } 
    } 
  
    // Main function that sorts arr[l..r] using 
    // merge() 
    static void sort(int arr[], int l, int r) 
    { 
        if (l < r) 
        { 
            // Find the middle point 
            int m = (l+r)/2; 
  
            // Sort first and second halves 
            sort(arr, l, m); 
            sort(arr , m+1, r); 
  
            // Merge the sorted halves 
            merge(arr, l, m, r); 
        } 
    } 
	static void merge(int arr[], int l, int m, int r) 
    { 
        // Find sizes of two subarrays to be merged 
        int n1 = m - l + 1; 
        int n2 = r - m; 
  
        /* Create temp arrays */
        int L[] = new int [n1]; 
        int R[] = new int [n2]; 
  
        /*Copy data to temp arrays*/
        for (int i=0; i<n1; ++i) 
            L[i] = arr[l + i]; 
        for (int j=0; j<n2; ++j) 
            R[j] = arr[m + 1+ j]; 
  
  
        /* Merge the temp arrays */
  
        // Initial indexes of first and second subarrays 
        int i = 0, j = 0; 
  
        // Initial index of merged subarry array 
        int k = l; 
        while (i < n1 && j < n2) 
        { 
            if (L[i] <= R[j]) 
            { 
                arr[k] = L[i]; 
                i++; 
            } 
            else
            { 
                arr[k] = R[j]; 
                j++; 
            } 
            k++; 
        } 
  
        /* Copy remaining elements of L[] if any */
        while (i < n1) 
        { 
            arr[k] = L[i]; 
            i++; 
            k++; 
        } 
  
        /* Copy remaining elements of R[] if any */
        while (j < n2) 
        { 
            arr[k] = R[j]; 
            j++; 
            k++; 
        } 
    } 
  
    // Main function that sorts arr[l..r] using 
    // merge() 
    static void sort(long arr[], int l, int r) 
    { 
        if (l < r) 
        { 
            // Find the middle point 
            int m = (l+r)/2; 
  
            // Sort first and second halves 
            sort(arr, l, m); 
            sort(arr , m+1, r); 
  
            // Merge the sorted halves 
            merge(arr, l, m, r); 
        } 
    } 
    static class Pair implements Comparable<Pair>{
        int a;
        int b;
        Pair(int a,int b){
            this.a=a;
 
            this.b=b;
        }   
        public int compareTo(Pair p){
            if(a>p.a)
                return 1;
            if(a==p.a)
                return (b-p.b);
            return -1;
        }
    }
	static class Reader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[128]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    } 
}