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:


class Graph:
    def __init__(self, n_vertices, edges, directed=True):
        self.n_vertices = n_vertices
        self.directed = directed
        self.edges = edges

    @property
    def adj(self):
        try:
            return self._adj
        except AttributeError:
            adj = [[] for _ in range(self.n_vertices)]
            if self.directed:
                for u,v in self.edges:
                    adj[u].append(v)
            else:
                for u,v in self.edges:
                    adj[u].append(v)
                    adj[v].append(u)
            self._adj = adj
            return adj


class RootedTree(Graph):
    def __init__(self, n_vertices, edges, root_vertex=0):
        """
        mode:
            'rerooting' -> initialize just enough to do rerooting dp
        """
        super().__init__(n_vertices, edges, directed=False)
        self.root = root_vertex


    @property
    def parent(self):
        try:
            return self._parent
        except AttributeError:
            adj = self.adj
            parent = [0]*self.n_vertices
            parent[self.root] = -1
            stack = [self.root]
            for _ in range(self.n_vertices):
                v = stack.pop()
                p = parent[v]
                for u in adj[v]:
                    if u != p:
                        parent[u] = v
                        stack.append(u)
            self._parent = parent
            return parent

    @property
    def children(self):
        try:
            return self._children
        except AttributeError:
            children = [None]*self.n_vertices
            for v,(l,p) in enumerate(zip(self.adj,self.parent)):
                children[v] = [u for u in l if u != p]
            self._children = children
            return children

    @property
    def dfs_order(self):
        try:
            return self._dfs_order
        except AttributeError:
            order = [0]*self.n_vertices
            children = self.children
            stack = [self.root]
            for i in range(self.n_vertices):
                v = stack.pop()
                order[i] = v
                for u in children[v]:
                    stack.append(u)
            self._dfs_order = order
            return order

def solve(edges, n):
    fib = [1,1]
    while fib[-1] < n:
        fib.append(fib[-1]+fib[-2])
    if fib[-1] != n:
        return False
    rt = RootedTree(n, edges)
    parent = rt.parent
    children = rt.children
    size = [0]*n

    stack = [(len(fib)-1, 0)]
    while stack:
        ind, root = stack.pop()
        if ind <= 3:
            continue
        split = [fib[ind-2],fib[ind-1]]

        s = [~root, root]
        while s:
            v = s.pop()
            if v < 0:
                v = ~v
                t = 1+sum(size[u] for u in children[v])
                size[v] = t
                p = parent[v]
                if t == split[0]:
                    stack.append((ind-2, v))
                    stack.append((ind-1, root))
                    children[p].remove(v)
                    parent[v] = -1
                    break
                elif t == split[1]:
                    stack.append((ind-1, v))
                    stack.append((ind-2, root))
                    children[p].remove(v)
                    parent[v] = -1
                    break
            else:
                for u in children[v]:
                    s.append(~u)
                    s.append(u)
        else:
            return False
    return True


import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline

m = map(int,read().split())

n = next(m)

edges = [(a-1,b-1) for a,b in zip(m,m)]

print('Yes' if solve(edges, n) else 'No')