Problem: Recently Vasya decided to improve his pistol shooting skills. Today his coach offered him the following exercise. He placed n cans in a row on a table. Cans are numbered from left to right from 1 to n. Vasya has to knock down each can exactly once to finish the exercise. He is allowed to choose the order in which he will knock the cans down.

Vasya knows that the durability of the i-th can is a_i. It means that if Vasya has already knocked x cans down and is now about to start shooting the i-th one, he will need (a_i ⋅ x + 1) shots to knock it down. You can assume that if Vasya starts shooting the i-th can, he will be shooting it until he knocks it down.

Your task is to choose such an order of shooting so that the number of shots required to knock each of the n given cans down exactly once is minimum possible.

Input

The first line of the input contains one integer n (2 ≤ n ≤ 1 000) — the number of cans.

The second line of the input contains the sequence a_1, a_2, ..., a_n (1 ≤ a_i ≤ 1 000), where a_i is the durability of the i-th can.

Output

In the first line print the minimum number of shots required to knock each of the n given cans down exactly once.

In the second line print the sequence consisting of n distinct integers from 1 to n — the order of indices of cans that minimizes the number of shots required. If there are several answers, you can print any of them.

Examples

Input


3
20 10 20


Output


43
1 3 2 


Input


4
10 10 10 10


Output


64
2 1 4 3 


Input


6
5 4 5 4 4 5


Output


69
6 1 3 5 2 4 


Input


2
1 4


Output


3
2 1 

Note

In the first example Vasya can start shooting from the first can. He knocks it down with the first shot because he haven't knocked any other cans down before. After that he has to shoot the third can. To knock it down he shoots 20 ⋅ 1 + 1 = 21 times. After that only second can remains. To knock it down Vasya shoots 10 ⋅ 2 + 1 = 21 times. So the total number of shots is 1 + 21 + 21 = 43.

In the second example the order of shooting does not matter because all cans have the same durability.

Solution (in JAVA):

Solution:
    import java.io.*;
    import java.util.*;
    import java.math.*;
    import java.lang.*;
     
     //@Manan Parmar

    public class Solution2 implements Runnable {


        public void run() {
            
            InputReader sc = new InputReader(System.in);
            PrintWriter out = new PrintWriter(System.out);
            
            int n=sc.nextInt(),a[]=new int[n];
            ArrayList<Integer> b=new ArrayList<Integer>();
            for(int i=0;i<n;i++)
            {
                a[i]=sc.nextInt();
                b.add(a[i]);
            }
            Arrays.sort(a);
            long sum=1;
            for(int i=n-2,j=1;i>=0;i--,j++)
                sum=sum+((a[i]*j)+1);
            out.println(sum);
            for(int i=n-1;i>=0;i--)
            {
                int x=b.indexOf(a[i]);
                out.println(x+1);
                b.set(x,0);
            } 
            out.close();
        }
     

    //========================================================================
        boolean check(char a,char b)
        {
            if(a==b)
                return true;
            else
                return false;
        }
        long binarySearch(long arr[], long x) 
        { 
            int l = 0, r = arr.length - 1,q=0; 
            while (l<=r) { 
                int m = l + (r - l) / 2; 
                if (arr[l] >=x) 
                {
                    q=1;
                    return l; 
                }
                if (arr[m] < x) 
                    l=m+1; 
                else
                    r=m;
            } 
            return -1;
        }

        static class InputReader {
            private InputStream stream;
            private byte[] buf = new byte[1024];
            private int curChar;
            private int numChars;
            private SpaceCharFilter filter;
            private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
     
            public InputReader(InputStream stream) {
                this.stream = stream;
            }
           
            public int read() {
                if (numChars==-1)
                    throw new InputMismatchException();
               
                if (curChar >= numChars) {
                    curChar = 0;
                    try {
                        numChars = stream.read(buf);
                    }
                    catch (IOException e) {
                        throw new InputMismatchException();
                    }
                   
                    if(numChars <= 0)              
                        return -1;
                }
                return buf[curChar++];
            }
         
            public String nextLine() {
                String str = "";
                try {
                    str = br.readLine();
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
                return str;
            }
            public int nextInt() {
                int c = read();
               
                while(isSpaceChar(c))
                    c = read();
               
                int sgn = 1;
               
                if (c == '-') {
                    sgn = -1;
                    c = read();
                }
               
                int res = 0;
                do {
                    if(c<'0'||c>'9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = read();
                }
                while (!isSpaceChar(c));
               
                return res * sgn;
            }
           
            public long nextLong() {
                int c = read();
                while (isSpaceChar(c))
                    c = read();
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = read();
                }
                long res = 0;
               
                do {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = read();
                }
                while (!isSpaceChar(c));
                    return res * sgn;
            }
           
            public double nextDouble() {
                int c = read();
                while (isSpaceChar(c))
                    c = read();
                int sgn = 1;
                if (c == '-') {
                    sgn = -1;
                    c = read();
                }
                double res = 0;
                while (!isSpaceChar(c) && c != '.') {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = read();
                }
                if (c == '.') {
                    c = read();
                    double m = 1;
                    while (!isSpaceChar(c)) {
                        if (c == 'e' || c == 'E')
                            return res * Math.pow(10, nextInt());
                        if (c < '0' || c > '9')
                            throw new InputMismatchException();
                        m /= 10;
                        res += (c - '0') * m;
                        c = read();
                    }
                }
                return res * sgn;
            }
           
            public String readString() {
                int c = read();
                while (isSpaceChar(c))
                    c = read();
                StringBuilder res = new StringBuilder();
                do {
                    res.appendCodePoint(c);
                    c = read();
                }
                while (!isSpaceChar(c));
               
                return res.toString();
            }
         
            public boolean isSpaceChar(int c) {
                if (filter != null)
                    return filter.isSpaceChar(c);
                return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
            }
         
            public String next() {
                return readString();
            }
           
            public interface SpaceCharFilter {
                public boolean isSpaceChar(int ch);
            }
        }

        public static void main(String args[]) throws Exception {
            new Thread(null, new Solution2(),"Main",1<<27).start();
        }
    }