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: Wrong Answer)

#include<bits/stdc++.h>
#define ll long long
#define rep(i,a,b) for(i=a;i<b;i++)
#define pb push_back
#define all(v) v.begin(),v.end()
#define F first
#define S second
#define vi vector < ll  int >
#define CLR(a) memset((a),0,sizeof(a))
#define mp make_pair
#define hell 1000000007
using namespace std;

 //int dp[1001][1001];
 /*
vector < int > tree(400005);

void buildtree (vector < int > v,int node,int start,int fin)
  {
      if(start==fin)
      {
          tree[node]=v[start];
          return;
      }
      int mid=(start+fin)/2;
      buildtree(v,2*node,start,mid);
      buildtree(v,2*node+1,mid+1,fin);
      tree[node]=tree[2*node]+tree[2*node+1];
  }

 int sum (int node,int tl,int tr,int l , int r)
   {
       if(l>r) return 0;
       if(l==tl and r==tr) return tree[node];
       int mid=(tl+tr)/2;
       return sum(2*node,tl,mid,l,min(r,mid))+sum(2*node+1,mid+1,tr,max(l,mid+1),r);
   }

  void update(int node,int tl , int tr,int pos,int val)
    {
        if(tl==tr) {tree[node]=val; return;}
        int mid=(tl+tr)/2;
        if(pos<=mid)
              update(2*node,tl,mid,pos,val);
        else
            update(2*node+1,mid+1,tr,pos,val);
        tree[node]=tree[2*node]+tree[2*node+1];

    }
string findSum(string str1, string str2)
{
    // Before proceeding further, make sure length
    // of str2 is larger.
    if (str1.length() > str2.length())
        swap(str1, str2);

    // Take an empty string for storing result
    string str = "";

    // Calculate length of both string
    int n1 = str1.length(), n2 = str2.length();

    // Reverse both of strings
    reverse(str1.begin(), str1.end());
    reverse(str2.begin(), str2.end());

    int carry = 0;
    for (int i=0; i<n1; i++)
    {
        // Do school mathematics, compute sum of
        // current digits and carry
        int sum = ((str1[i]-'0')+(str2[i]-'0')+carry);
        str.push_back(sum%10 + '0');

        // Calculate carry for next step
        carry = sum/10;
    }

    // Add remaining digits of larger number
    for (int i=n1; i<n2; i++)
    {
        int sum = ((str2[i]-'0')+carry);
        str.push_back(sum%10 + '0');
        carry = sum/10;
    }

    // Add remaining carry
    if (carry)
        str.push_back(carry+'0');

    // reverse resultant string
    reverse(str.begin(), str.end());

    return str;
}
*/


void solve()
{
    ll int i,j=0,r=200,p,q,k,d,y=0,h,flag=1,n,m=0,a=hell,b=hell,id,h1,h2,a1,b1,a2,w,x,u,f,l;
   cin>>n;
    y=(1<<n);
    vi v(y);
    //y=0;
    map < ll , ll > M;
rep(i,0,y) cin>>v[i],M[v[i]]++;
  //map < ll, ll > :: iterator it;
  j=1; k=1;
  for(auto it=M.rbegin();it!=M.rend();++it)
  {
      if(it->second>k*(k-1)/2) {cout<<"No"; return;}
      k++;
      it++;
  }
  cout<<"Yes";

}


signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int t=1;
   // cin>>t;
    while(t--)
     solve();
}