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 <set>
#include <cstdio>
#include <algorithm>
using namespace std;
const int Maxn=200000;
int n;
int head[Maxn+5],arrive[Maxn<<1|5],nxt[Maxn<<1|5],tot;
void add_edge(int from,int to){
	arrive[++tot]=to;
	nxt[tot]=head[from];
	head[from]=tot;
}
int lis[Maxn+5];
int dfn[Maxn+5],dfn_tot;
int fa[Maxn+5];
set<pair<int,int> > st[Maxn+5];
int level[Maxn+5];
void init_dfs(int u){
	dfn[u]=++dfn_tot;
	lis[dfn[u]]=u;
	for(int i=head[u];i;i=nxt[i]){
		int v=arrive[i];
		if(v==fa[u]){
			continue;
		}
		fa[v]=u;
		init_dfs(v);
	}
}
void merge(set<pair<int,int> > &x,set<pair<int,int> > &y){
	set<pair<int,int> >::iterator it=y.begin();
	while(it!=y.end()){
		x.insert(*it);
		it++;
	}
	y.clear();
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<n;i++){
		int u,v;
		scanf("%d%d",&u,&v);
		add_edge(u,v);
		add_edge(v,u);
	}
	init_dfs(1);
	for(int i=1;i<=n;i++){
		level[i]=1;
	}
	for(int i=n;i>0;i--){
		int u=lis[i];
		set<pair<int,int> >::iterator it=st[u].begin();
		while(!st[u].empty()){
			it=st[u].begin();
			if((level[u]==1&&(it->first)==1)||level[u]-(it->first)==1){
				level[u]++;
				int id=(it->second);
				st[u].erase(it);
				merge(st[u],st[id]);
			}
			else{
				break;
			}
		}
		if(fa[u]){
			st[fa[u]].insert(make_pair(level[u],u));
		}
	}
	while(!st[1].empty()){
		set<pair<int,int> >::iterator it=st[1].begin();
		if(abs(level[1]-(it->first))==1){
			level[1]=max(level[1],(it->first)+1);
			int id=(it->second);
			st[1].erase(it);
			merge(st[1],st[id]);
		}
		else{
			break;
		}
	}
	if(st[1].empty()){
		puts("YES");
	}
	else{
		puts("NO");
	}
	return 0;
}
*/
#include <cstdio>
const int Maxn=200000;
int n;
int head[Maxn+5],arrive[Maxn<<1|5],nxt[Maxn<<1|5],tot;
void add_edge(int from,int to){
	arrive[++tot]=to;
	nxt[tot]=head[from];
	head[from]=tot;
}
bool del[Maxn+5];
int find_id(int x){
	return ((x-1)>>1)+1;
}
int f[Maxn+5];
int len;
int sz[Maxn+5];
int fa_id[Maxn+5],fa[Maxn+5];
int lis[Maxn+5],lis_len;
void sz_dfs(int u){
	lis[++lis_len]=u;
	sz[u]=1;
	for(int i=head[u];i;i=nxt[i]){
		if(del[find_id(i)]){
			continue;
		}
		int v=arrive[i];
		if(v==fa[u]){
			continue;
		}
		fa[v]=u;
		fa_id[v]=find_id(i);
		sz_dfs(v);
		sz[u]+=sz[v];
	}
}
bool calc(int u,int id){
	if(id<=2){
		return 1;
	}
	lis_len=0;
	fa[u]=fa_id[u]=0;
	sz_dfs(u);
	for(int i=1;i<=lis_len;i++){
		if(sz[lis[i]]==f[id-1]||sz[lis[i]]==f[id-2]){
			del[fa_id[lis[i]]]=1;
			if(sz[lis[i]]==f[id-1]){
				int x=lis[i],y=fa[x];
				return calc(x,id-1)&&calc(y,id-2);
			}
			else{
				int x=lis[i],y=fa[x];
				return calc(x,id-2)&&calc(y,id-1);
			}
			return 0;
		}
	}
	return 0;
}
int main(){
	scanf("%d",&n);
	if(n==1){
		puts("YES");
		return 0;
	}
	f[0]=f[1]=1;
	for(len=2;(f[len]=f[len-1]+f[len-2])<n;len++);
	if(f[len]>n){
		puts("NO");
		return 0;
	}
	for(int i=1;i<n;i++){
		int u,v;
		scanf("%d%d",&u,&v);
		add_edge(u,v);
		add_edge(v,u);
	}
	if(calc(1,len)){
		puts("YES");
	}
	else{
		puts("NO");
	}
	return 0;
}