int n=5;
        vector<int>v(n);
        for(int i=0;i<n;i++){
            v[i]=i+1;
        }
        map<string,int>mp;
        for(int i=0;i<120;i++){
            string str;
            for(int i=0;i<4;i++){
                if(v[i+1]>v[i]){
                    str+=('1');
                }else{
                    str+=('0');
                }
            }
            next_permutation(all(v));
            mp[str]++;
        }
        for(auto [x,y]: mp){
            cout<<x<<' '<<y<<"\n";
        }

0000 1
0001 4
0010 9
0011 6
0100 9
0101 16
0110 11
0111 4
1000 4
1001 11
1010 16
1011 9
1100 6
1101 9
1110 4
1111 1

Some pattern we can observe. But can we predict the actual number of these string ??