Problem: Let F_k denote the k-th term of Fibonacci sequence, defined as below:

  * F_0 = F_1 = 1
  * for any integer n ≥ 0, F_{n+2} = F_{n+1} + F_n



You are given a tree with n vertices. Recall that a tree is a connected undirected graph without cycles.

We call a tree a Fib-tree, if its number of vertices equals F_k for some k, and at least one of the following conditions holds:

  * The tree consists of only 1 vertex;
  * You can divide it into two Fib-trees by removing some edge of the tree. 



Determine whether the given tree is a Fib-tree or not.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of vertices in the tree.

Then n-1 lines follow, each of which contains two integers u and v (1≤ u,v ≤ n, u ≠ v), representing an edge between vertices u and v. It's guaranteed that given edges form a tree.

Output

Print "YES" if the given tree is a Fib-tree, or "NO" otherwise.

You can print your answer in any case. For example, if the answer is "YES", then the output "Yes" or "yeS" will also be considered as correct answer.

Examples

Input


3
1 2
2 3


Output


YES


Input


5
1 2
1 3
1 4
1 5


Output


NO


Input


5
1 3
1 2
4 5
3 4


Output


YES

Note

In the first sample, we can cut the edge (1, 2), and the tree will be split into 2 trees of sizes 1 and 2 correspondently. Any tree of size 2 is a Fib-tree, as it can be split into 2 trees of size 1.

In the second sample, no matter what edge we cut, the tree will be split into 2 trees of sizes 1 and 4. As 4 isn't F_k for any k, it's not Fib-tree.

In the third sample, here is one possible order of cutting the edges so that all the trees in the process are Fib-trees: (1, 3), (1, 2), (4, 5), (3, 4). 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
//#define int long long
#define ii pair<int,int>
#define F first
#define S second
#define du long double
using namespace std;
const int N=2e5+100;
int feb[N];
bool f[N];
int a[N];
vector<vector<int>> vec;
vector<int> g[N];
vector<int> st;
vector<int> st1;
vector<int> st2;
bool is_st[N];
bool is_st1[N];
bool is_st2[N];
int v1,v2,sz;
void dfs2(int u,int p)
{
    st1.push_back(u);
    is_st1[u]=1;
    for(auto x:g[u]){
        if(is_st[x]==0)continue;
        if(x==p)continue;
        dfs2(x,u);
    }
}
void dfs(int u,int p)
{
    int ret=1;
    for(auto x:g[u]){
        if(is_st[x]==0)continue;
        if(x==p)continue;
        dfs(x,u);
    }
    for(auto x:g[u]){
        if(is_st[x]==0)continue;
        if(x==p)continue;
        ret+=a[x];
    }
    a[u]=ret;
    for(auto x:g[u]){
        if(is_st[x]==0)continue;
        if(x==p)continue;
        if(f[sz-a[x]]&&f[a[x]]){
            v1=x;
            v2=u;
        }
    }
}
void fix(int u)
{
    for(auto x:st)a[x]=0;
    v1=0;v2=0;
    dfs(u,u);
//    cout<<v1<<" "<<v2<<endl;
    if(v1)dfs2(v1,v2);
    for(auto x:st){
        if(is_st1[x]==0){
            st2.push_back(x);
            is_st2[x]=1;
        }
    }
}
void solve()
{
    feb[0]=1;
    feb[1]=1;
    for(int i=2;feb[i-1]<N;i++){
        feb[i]=feb[i-1]+feb[i-2];
    }
    int n,idx;
    cin>>n;
    for(int i=1;i<n;i++){
        int a,b;
        scanf("%d",&a);
        scanf("%d",&b);
        g[a].push_back(b);
        g[b].push_back(a);
    }
    for(int i=1;;i++){
        f[feb[i]]=1;
        if(feb[i]==n){
            break;
        }
        if(feb[i]>n){
            cout<<"NO";
            return;
        }
    }
    for(int i=1;i<=n;i++){
        st.push_back(i);
    }
    vec.push_back(st);
    while(vec.empty()==0){
        for(auto x:st){
            is_st[x]=0;
        }
        for(auto x:st1){
            is_st1[x]=0;
        }
        for(auto x:st2){
            is_st2[x]=0;
        }
        st.clear();
        st1.clear();
        st2.clear();
        st=vec.back();
      //  for(auto x:st)cout<<x<<" ";cout<<endl;
        vec.pop_back();
        if(st.size()<=3)continue;
        int x=st[0];
        sz=st.size();
        for(auto x:st)is_st[x]=1;
        fix(x);
        int sz1=st1.size();
        int sz2=st2.size();
        if(f[sz1]==0||f[sz2]==0){
//            cout<<"wrong\n\n";
  //          for(auto x:st1)cout<<x<<" ";cout<<endl;
    //        for(auto x:st2)cout<<x<<" ";cout<<endl;
            cout<<"NO";
            return;
        }
        vec.push_back(st1);
        vec.push_back(st2);
    }
    cout<<"YES\n";
}

int main()
{
    //freopen(".in","r",stdin);freopen(".out","w",stdout);
    int t=1;
//    cin>>t;
    while(t--)solve();
}