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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskE solver = new TaskE();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskE {
        final int[] fib = new int[29];
        int[] whichFib;

        {
            fib[1] = 1;
            for (int i = 2; i < fib.length; i++) {
                fib[i] = fib[i - 1] + fib[i - 2];
            }
//        System.out.println(Arrays.toString(fib));
            int last = fib[fib.length - 1];
            whichFib = new int[last + 1];
            Arrays.fill(whichFib, -1);
            for (int i = 1; i < fib.length; i++) {
                whichFib[fib[i]] = i;
            }
        }

        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.nextInt();
            if (fib[fib.length - 1] <= n) {
                throw new AssertionError();
            }

            Graph g = new Graph(n);
            for (int i = 0; i < n - 1; i++) {
                int u = in.nextInt() - 1;
                int v = in.nextInt() - 1;
                g.addEdge(u, v);
                g.addEdge(v, u);
            }

            out.println(ok(g) ? "YES" : "NO");
        }

        private boolean ok(Graph g) {
            int k = whichFib[g.n];
            if (k < 0) {
                return false;
            }
            if (g.n == 1) {
                return true;
            }
            int[] subtreeSize = new int[g.n];
            int[] parent = new int[g.n];
            parent[0] = -1;
            boolean[] mark = new boolean[g.n];
            dfs(g, subtreeSize, parent, mark, 0);
            int cut = -1;
            for (int i = 0; i < g.n; i++) {
                if (subtreeSize[i] == fib[k - 1] || subtreeSize[i] == fib[k - 2]) {
                    cut = i;
                }
            }
            if (cut < 0) {
                return false;
            }
            Arrays.fill(mark, false);
            dfs(g, subtreeSize, parent, mark, cut);
            Graph g0 = new Graph(subtreeSize[cut]);
            Graph g1 = new Graph(g.n - subtreeSize[cut]);
            int[] id = new int[g.n];
            int[] last = new int[2];
            for (int i = 0; i < g.n; i++) {
                if (mark[i]) {
                    id[i] = last[0]++;
                } else {
                    id[i] = last[1]++;
                }
            }
            for (int i = 1; i < g.n; i++) {
                int j = parent[i];
                if (mark[i] != mark[j]) {
                    continue;
                }
                if (mark[i]) {
                    g0.addEdge(id[i], id[j]);
                    g0.addEdge(id[j], id[i]);
                } else {
                    g1.addEdge(id[i], id[j]);
                    g1.addEdge(id[j], id[i]);
                }
            }
            return ok(g0) && ok(g1);
        }

        private void dfs(Graph g, int[] subtreeSize, int[] parent, boolean[] mark, int v) {
            subtreeSize[v] = 1;
            mark[v] = true;
            for (int e = g.firstEdge[v]; e >= 0; e = g.edgeNxt[e]) {
                int u = g.edgeDst[e];
                if (u == parent[v]) {
                    continue;
                }
                parent[u] = v;
                dfs(g, subtreeSize, parent, mark, u);
                subtreeSize[v] += subtreeSize[u];
            }
        }

        class Graph {
            int[] firstEdge;
            int[] edgeNxt;
            int[] edgeDst;
            int numEdges;
            int n;

            Graph(int n) {
                this.n = n;
                firstEdge = new int[n];
                Arrays.fill(firstEdge, -1);
                final int initialCapacity = 10;
                edgeNxt = new int[initialCapacity];
                edgeDst = new int[initialCapacity];
                numEdges = 0;
            }

            void addEdge(int a, int b) {
                int e = numEdges++;
                if (e >= edgeNxt.length) {
                    reallocate();
                }
                edgeNxt[e] = firstEdge[a];
                edgeDst[e] = b;
                firstEdge[a] = e;
            }

            void reallocate() {
                int k = edgeNxt.length;
                k = 3 * k / 2;
                edgeNxt = Arrays.copyOf(edgeNxt, k);
                edgeDst = Arrays.copyOf(edgeDst, k);
            }

        }

    }

    static class FastScanner {
        private BufferedReader in;
        private StringTokenizer st;

        public FastScanner(InputStream stream) {
            in = new BufferedReader(new InputStreamReader(stream));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    String rl = in.readLine();
                    if (rl == null) {
                        return null;
                    }
                    st = new StringTokenizer(rl);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

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

    }
}