Problem:
Score : 600 points

Problem Statement

We have one slime.

You can set the health of this slime to any integer value of your choice.

A slime reproduces every second by spawning another slime that has strictly less health. You can freely choose the health of each new slime. The first reproduction of our slime will happen in one second.

Determine if it is possible to set the healths of our first slime and the subsequent slimes spawn so that the multiset of the healths of the 2^N slimes that will exist in N seconds equals a multiset S.

Here S is a multiset containing 2^N (possibly duplicated) integers: S_1,~S_2,~...,~S_{2^N}.

Constraints

All values in input are integers.

1 \leq N \leq 18

1 \leq S_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
S_1 S_2 ... S_{2^N}

Output

If it is possible to set the healths of the first slime and the subsequent slimes spawn so that the multiset of the healths of the 2^N slimes that will exist in N seconds equals S, print Yes; otherwise, print No.

Sample Input 1

2
4 2 3 1

Sample Output 1

Yes

We will show one way to make the multiset of the healths of the slimes that will exist in 2 seconds equal to S.

First, set the health of the first slime to 4.

By letting the first slime spawn a slime whose health is 3, the healths of the slimes that exist in 1 second can be 4,~3.

Then, by letting the first slime spawn a slime whose health is 2, and letting the second slime spawn a slime whose health is 1, the healths of the slimes that exist in 2 seconds can be 4,~3,~2,~1, which is equal to S as multisets.

Sample Input 2

2
1 2 3 1

Sample Output 2

Yes

S may contain multiple instances of the same integer.

Sample Input 3

1
1 1

Sample Output 3

No

Sample Input 4

5
4 3 5 3 1 2 7 8 7 4 6 3 7 2 3 6 2 7 3 2 6 7 3 4 6 7 3 4 2 5 2 3

Sample Output 4

No

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp> // Common file 
#include <ext/pb_ds/tree_policy.hpp> 
#include <functional> // for less 
#define pb push_back
#define For(i,s,e) for (ll i=(s); i<(e); i++)
#define Debug_array(a,n) for (ll i=(0); i<(n); i++) cout<<a[i]<<" "
#define Foe(i,s,e) for (ll i=(s); i<=(e); i++)
#define Fod(i,s,e) for (ll i=(s)-1; i>=(e); i--)
#define pii pair<ll,ll>
#define fi first
#define se second
#define endl "\n"
#define mp make_pair
#define big_prime 15486277
#define bigger_prime 179424697
#define biggest_prime 32416188691
//#define random_shuffle(indices.begin(), indices.end());
//std::random_device rd;
//std::mt19937 g(rd());
//std::shuffle(v.begin(), v.end(), g);
using namespace __gnu_pbds; 
using namespace std;
template <class T> ostream& operator << (ostream &os, const vector<T> &v) { for (T i : v) os << i << ' '; return os; }
template <class T> ostream& operator << (ostream &os, const set<T> &v) { for (T i : v) os << i << ' '; return os; }
template <class T, class S> ostream& operator << (ostream &os, const pair<T, S> &v) { os << v.first << ' ' << v.second; return os; }
// template <class T, class S> ostream& operator << (ostream &os, const unordered_map<T, S> &v) { for (auto i : v) os << '(' << i.first << "=>" << i.second << ')' << ' '; return os; }
 
#ifndef ONLINE_JUDGE
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
    template <class Arg1> void __f(const char* name, Arg1&& arg1) { cerr << name << " : " << arg1 << endl; }
    template <class Arg1, class... Args>
    void __f(const char* names, Arg1&& arg1, Args&&... args) {
        const char* sep = strchr(names + 1, ',');
        cerr.write(names, sep - names) << " : " << arg1 << "  ";
        __f(sep + 1, args...);
    }
#else
#define trace(...) 0
#define _CRT_SECURE_NO_WARNINGS
#endif // ifndef ONLINE_JUDGE


typedef long long ll;
typedef tree<ll, null_type, less<ll>, rb_tree_tag,tree_order_statistics_node_update> ordered_set; 

#define Mod 1000000007
#define MAX 5002

vector<ll> done;
multiset<ll> s;
int main(){
	ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
	
	ll n;cin>>n;
	ll a[(1<<n)+1];For(i,1,(1<<n)+1) cin>>a[i];
	sort(a+1,a+(1<<n)+1,greater<ll>());

	For(i,1,(1<<n)+1) s.insert(-1*a[i]);

	done.pb((*s.begin())*-1);
	s.erase(s.begin());

	while(s.size()>0){
		for(ll x:done){
			multiset<ll>::iterator it1 = s.upper_bound(-1*x);
			if(it1==s.end()){
				cout<<"No"<<endl;
				return 0;
			}
			done.pb((*it1)*(-1));
			s.erase(it1);
			if(s.size()==0) break;
		}
	}
	cout<<"Yes"<<endl;































	
}