Problem: The only difference between easy and hard versions is a number of elements in the array.

You are given an array a consisting of n integers. The value of the i-th element of the array is a_i.

You are also given a set of m segments. The j-th segment is [l_j; r_j], where 1 ≤ l_j ≤ r_j ≤ n.

You can choose some subset of the given set of segments and decrease values on each of the chosen segments by one (independently). For example, if the initial array a = [0, 0, 0, 0, 0] and the given segments are [1; 3] and [2; 4] then you can choose both of them and the array will become b = [-1, -2, -2, -1, 0].

You have to choose some subset of the given segments (each segment can be chosen at most once) in such a way that if you apply this subset of segments to the array a and obtain the array b then the value max_{i=1}^{n}b_i - min_{i=1}^{n}b_i will be maximum possible.

Note that you can choose the empty set.

If there are multiple answers, you can print any.

If you are Python programmer, consider using PyPy instead of Python when you submit your code.

Input

The first line of the input contains two integers n and m (1 ≤ n ≤ 300, 0 ≤ m ≤ 300) — the length of the array a and the number of segments, respectively.

The second line of the input contains n integers a_1, a_2, ..., a_n (-10^6 ≤ a_i ≤ 10^6), where a_i is the value of the i-th element of the array a.

The next m lines are contain two integers each. The j-th of them contains two integers l_j and r_j (1 ≤ l_j ≤ r_j ≤ n), where l_j and r_j are the ends of the j-th segment.

Output

In the first line of the output print one integer d — the maximum possible value max_{i=1}^{n}b_i - min_{i=1}^{n}b_i if b is the array obtained by applying some subset of the given segments to the array a.

In the second line of the output print one integer q (0 ≤ q ≤ m) — the number of segments you apply.

In the third line print q distinct integers c_1, c_2, ..., c_q in any order (1 ≤ c_k ≤ m) — indices of segments you apply to the array a in such a way that the value max_{i=1}^{n}b_i - min_{i=1}^{n}b_i of the obtained array b is maximum possible.

If there are multiple answers, you can print any.

Examples

Input


5 4
2 -2 3 1 2
1 3
4 5
2 5
1 3


Output


6
2
1 4 


Input


5 4
2 -2 3 1 4
3 5
3 4
2 4
2 5


Output


7
2
3 2 


Input


1 0
1000000


Output


0
0

Note

In the first example the obtained array b will be [0, -4, 1, 1, 2] so the answer is 6.

In the second example the obtained array b will be [2, -3, 1, -1, 4] so the answer is 7.

In the third example you cannot do anything so the answer is 0.

Solution (in JAVA):

Solution:
import java.util.*;

import javax.lang.model.util.ElementScanner6;

import java.io.*;

public class Main{

    public static void main(String[] args) {

        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader inp = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
        solver.solve(inp, out);
        out.close();
        
        }



    static class Solver {


        class Node implements Comparable<Node>{
            int l;
            int r;
        
            Node(int l,int r)
            {
                this.l = l;
                this.r =r;
                

            }

        public int compareTo(Node n)
            {
                return Long.compare(this.l, n.l);
            }
        }

        public boolean done(int[] sp,int[] par)
        {
            int root;

            root=findSet(sp[0],par);
            
        for(int i=1;i<sp.length;i++)
        {
                if(root!=findSet(sp[i], par))
                    return false;
        }
        return true;
        }
    public int findSet(int i,int[] par)
    {
        int x =i;
            boolean flag =false;
            while(par[i]>=0)
            {
                flag = true;
                i=par[i];
            }
            if(flag)
                par[x]=i;
            return i;
    }

    public void unionSet(int i,int j,int[] par)
    {
            int x = findSet(i, par);
            int y = findSet(j, par);
            if(x<y)
            {
                par[y]=x;
            }
            else
            {
                par[x]=y;
            }
    }

    public  long pow(long a, long b, long MOD) {
            if (b == 0) {
                return 1;
            }
            if (b == 1) {
                return a;
            }
            long val = pow(a, b / 2, MOD);
            if (b % 2 == 0) {
                return val * val % MOD;
            } else {
                return val * (val * a % MOD) % MOD;

            }
        
        }


        public void minPrimeFactor(int n,int[] s)
        {
            boolean prime[] = new boolean[n+1];
            Arrays.fill(prime, true);
            s[1]=1;
            s[2]=2;
            for(int i=4;i<=n;i+=2)
            {
                prime[i]=false;
                s[i]=2;
            }

            for(int i=3;i<=n;i+=2)
            {
                if(prime[i])
                {
                    s[i]=i;
                    for(int j=2*i;j<=n;j+=i)
                    {
                        prime[j]=false;
                        s[j]=i;
                    }
                }
            }
            
        }

        
        // public void findAllPrime(int n,ArrayList<Node> al,int s[])
        // {
        //     int curr = s[n];
        //     int cnt = 1;
        //     while(n>1)
        //     {
        //         n/=s[n];
        //         if(curr==s[n])
        //         {
        //             cnt++;
        //             continue;

        //         }
        //         Node n1 = new Node(curr,cnt);
        //         al.add(n1);

        //         curr=s[n];
        //         cnt=1;
        //     }
        // }

        

        public int binarySearch(int n,int k)
        {
            int left=1;
            int right=100000000+5;
            int ans=0;
            while(left<=right)
            {
                int mid = (left+right)/2;
                if(n/mid>=k)
                {
                    left = mid+1;
                    ans=mid;
                }
                else
                {
                    right=mid-1;
                }
            }

            return ans;
        }
        public boolean checkPallindrom(String s)
        {
            char ch[] = s.toCharArray();

            for(int i=0;i<s.length()/2;i++)
            {
                if(ch[i]!=ch[s.length()-1-i])
                    return false;
            }
            return true;
        }


        public void dfs_util(ArrayList<Integer>[] al,boolean vis[],int x,int cnt[],int sts[],int fts[],long sv[])
        {
                
            vis[x] = true;
            long min=Long.MAX_VALUE;
                sts[cnt[0]]=x+1;
                for(int i=0;i<al[x].size();i++)
                {
                    
                    if(!vis[al[x].get(i)])
                    {
                        cnt[0]++;
                        dfs_util(al, vis, al[x].get(i),cnt,sts,fts,sv);
                        if(sv[al[x].get(i)]<min&&sv[al[x].get(i)]!=-1)
                        {
                            min=sv[al[x].get(i)];
                        }
                        
                        
                    }    
                    
                }

            
                if(sv[x]==-1)
                {
                    if(min==Long.MAX_VALUE)
                    {
                        min=-1;
                    }
                    sv[x]=min;
                }
            
            
            return ;
        }

        public void dfs(ArrayList[] al,int sts[],int fts[],long sv[])
        {
            
        boolean vis[] = new boolean[al.length];
        int cnt[]= new int[2*al.length+2];
        for(int i=0;i<al.length;i++)
        {
                if(!vis[i])
                {
                    
                    dfs_util(al,vis,i,cnt,sts,fts,sv);
                }
        }
        }

        public void remove(ArrayList<Integer>[] al,int x)
        {
            for(int i=0;i<al.length;i++)
            {
                for(int j=0;j<al[i].size();j++)
                {

                    if(al[i].get(j)==x)
                        al[i].remove(j);

                }
            }
        }

        public int gcd(int a, int b) 
        { 
            if (a == 0) 
                return b; 
            return gcd(b % a, a); 
        }


        public void printDivisors(int n,ArrayList<Integer> al) 
        { 
            // Note that this loop runs till square root 
            for (int i=1; i<=Math.sqrt(n); i++) 
            { 
                if (n%i==0) 
                { 
                    // If divisors are equal, print only one 
                    if (n/i == i) 
                    {
                        al.add(i);
                    }
                      
        
                    else // Otherwise print both 
                    {
                        al.add(i);
                        al.add(n/i);
                    }
                        
                } 
            } 
        } 

        private void solve(InputReader inp, PrintWriter out1) {
               int n = inp.nextInt();
               int m = inp.nextInt();
               int arr[] = new int[n];

               for(int i=0;i<n;i++)
               {
                   arr[i] = inp.nextInt();
               }

               ArrayList<Integer> ans  = new ArrayList<Integer>();
               int ans1=0;
               int min=Integer.MAX_VALUE;
               int max = Integer.MIN_VALUE;
               for(int i=0;i<n;i++)
               {
                    min=Integer.min(min, arr[i]);
                    max = Integer.max(max,arr[i]);
               }
               ans1 = max-min;

               Node seg[] = new Node[m];
               
               for(int i=0;i<m;i++)
               {
                   int l = inp.nextInt();
                   int r = inp.nextInt();
                   l--;
                   r--;
                   seg[i] = new Node(l,r);
               }

               ArrayList<Integer> al[]= new ArrayList[n];
               int pos=-1;

               for(int i=0;i<n;i++)
               {
                al[i] = new ArrayList<Integer>();
               }

               for(int i=0;i<n;i++)
               {
                   int arr1[] = Arrays.copyOf(arr, arr.length);
                   for(int j=0;j<m;j++)
                   {
                        int l = seg[j].l;
                        int r = seg[j].r;

                        if(i>=l&&i<=r)
                        {
                            for(int k=l;k<=r;k++)
                            {
                                arr1[k]--;
                            }
                            al[i].add(j);
                        }

                   }
                   Arrays.sort(arr1);
                //    out1.println(Arrays.toString(arr1));
                   if(arr1[arr1.length-1]-arr1[0]>ans1)
                   {
                       ans1=arr1[arr1.length-1]-arr1[0];
                       pos=i;

                   }
               }
               out1.println(ans1);
               if(pos==-1)
               {
                   out1.println(0);
                //    out1.println(0);
                   return;
               }
            //    out1.println("pos "+pos);
               out1.println(al[pos].size());
               for(int i=0;i<al[pos].size();i++)
               {
                    out1.print((al[pos].get(i)+1)+" ");
               }

               
               
               
               

            }

}





    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }
    }
}
class ele{
    long value;
    long i;
    boolean flag;
    public ele(long value,long i)
    {
        this.value = value;
        this.i=i;
        this.flag = false;
    }
}