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 PYTHON3):

Solution:
import io
import os

from collections import Counter, defaultdict, deque


def solve(N, edges):
    fib = [1, 1]
    while fib[-1] < N:
        fib.append(fib[-2] + fib[-1])
    fibToIndex = {x: i for i, x in enumerate(fib)}

    if N not in fibToIndex:
        return "NO"

    graph = [set() for i in range(N)]
    for u, v in edges:
        graph[u].add(v)
        graph[v].add(u)

    root = 0
    q = [root]
    parent = [-1] * N
    parent[root] = -1
    for u in q:
        for v in graph[u]:
            if v != parent[u]:
                parent[v] = u
                q.append(v)

    subTreeSize = [-1] * N
    for u in q[::-1]:
        count = 1
        for v in graph[u]:
            if v != parent[u]:
                count += subTreeSize[v]
        subTreeSize[u] = count

    def isFib(root, numNodes):
        if numNodes <= 3:
            return True

        i = fibToIndex[numNodes]
        F1 = fib[i - 1]
        F2 = fib[i - 2]

        q = deque([root])
        while q:
            u = q.popleft()
            count = subTreeSize[u]
            if count == F1 or count == F2:
                uSize = F1 if count == F1 else F2
                p = parent[u]
                graph[u].remove(p)
                graph[p].remove(u)
                parent[u] = -1
                while parent[p] != -1:
                    subTreeSize[p] -= count
                    p = parent[p]
                return isFib(u, uSize) and isFib(p, numNodes - uSize)

            for v in graph[u]:
                if v != parent[u]:
                    q.append(v)
        return False

    if isFib(root, N):
        return "YES"
    return "NO"


DEBUG = False
if DEBUG:
    N = 196418
    edges = []
    for i in range(N - 1):
        edges.append((i, i + 1))
    ans = solve(N, edges)
    print(ans)
    exit()


if __name__ == "__main__":
    input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline

    TC = 1
    for tc in range(1, TC + 1):
        (N,) = [int(x) for x in input().split()]
        edges = [[int(x) - 1 for x in input().split()] for i in range(N - 1)]

        ans = solve(N, edges)
        print(ans)