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 JAVA):

Solution:
import java.util.*;
import java.io.*;

public class E1491 {
	static ArrayList<Edge>[] adjList;
	static int[] subTree;
	static int[] fib;

	static class Edge {
		int u, v;
		boolean valid;
		int myNode, mySize;

		public Edge(int u, int v) {
			this.u = u;
			this.v = v;
			valid = true;
		}

		int other(int x) {
			return u ^ v ^ x;
		}

		void close() {
			valid = false;
		}

	}

	public static Edge dfs(int u, int p, int size, Edge cur) {
		subTree[u] = 1;
		Edge ans = null;
		for (Edge e : adjList[u]) {
			if (!e.valid)
				continue;
			int x = e.other(u);
			if (x != p) {
				Edge c = dfs(x, u, size, e);
				if (c != null)
					ans = c;
				subTree[u] += subTree[x];
			}
		}
		if (subTree[u] == fib[size - 1]) {
			ans = cur;
			ans.myNode = u;
			ans.mySize = size - 1;
		} else if (subTree[u] == fib[size - 2]) {
			ans = cur;
			ans.myNode = u;
			ans.mySize = size - 2;
		}
		return ans;
	}

	public static boolean solve(int u, int size) {
		if (fib[size] <= 3)
			return true;
		Edge x = dfs(u, -1, size, null);
		if (x == null)
			return false;
		x.close();
		return solve(x.myNode, x.mySize) && solve(x.other(x.myNode), (x.mySize == size - 1 ? size - 2 : (size - 1)));
	}

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int n = sc.nextInt();
		adjList = new ArrayList[n];
		for (int i = 0; i < adjList.length; i++) {
			adjList[i] = new ArrayList<Edge>();
		}
		for (int i = 0; i < n - 1; i++) {
			int u = sc.nextInt() - 1;
			int v = sc.nextInt() - 1;
			Edge e = new Edge(u, v);
			adjList[u].add(e);
			adjList[v].add(e);
		}
		subTree = new int[n];
		fib = new int[30];
		fib[0] = 1;
		fib[1] = 1;
		for (int i = 2; i < fib.length; i++) {
			fib[i] = fib[i - 1] + fib[i - 2];
		}
//		pw.println(Arrays.toString(fib));
		int size = -1;
		for (int i = 0; i < fib.length; i++) {
			if (fib[i] == n) {
				size = i;
			}
		}
		if (size == -1) {
			pw.println("NO");
		} else {
			pw.println(solve(0, size) ? "YES" : "NO");
		}
		pw.close();

	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(FileReader f) {
			br = new BufferedReader(f);
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public int[] nextIntArr(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = Integer.parseInt(next());
			}
			return arr;
		}

	}

}