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 <bits/stdc++.h>
#ifdef ALGO
#include "el_psy_congroo.hpp"
#else
#define DUMP(...) 1145141919810
#define CHECK(...) (__VA_ARGS__)
#endif

const int kN = 200000 + 5;
const int kM = 27;
std::vector<int> fib{1, 1};

int fib_id[kN];

struct Edge {
  int v;
  int id;
};

int n, m;
std::vector<Edge> edges[kN];
std::map<int, bool> f[kN];
int sz[kN], parent[kN];

bool ban[kN];

struct Candidate {
  int u;
  int fa;
  int id;
  int size;
  bool is_full;
};

void find_candidate(int u, int fa, int id, int target_a, int target_b, std::vector<Candidate>& candidates) {
  Candidate cur{.u = u, .fa = fa, .id = id, .size = 1, .is_full = true};
  for (const Edge& e : edges[u]) if (e.v != fa) {
    if (ban[e.id]) {
      cur.is_full = false;
    } else {
      find_candidate(e.v, u, e.id, target_a, target_b, candidates);
      cur.is_full &= candidates.back().is_full;
      cur.size += candidates.back().size;
      if (candidates.back().size != target_a && candidates.back().size != target_b) {
        candidates.pop_back();
      }
    }
  }
  candidates.emplace_back(std::move(cur));
}

bool search(int u, int fa, int size, bool is_full) {
  if (fib_id[size] == -1) return false;
  if (is_full) {
    auto it = f[u].find(fa);
    if (it != f[u].end()) {
      return it->second;
    }
  }
  bool ret = false;
  if (size == 1) {
    bool single = true;
    for (const Edge& e : edges[u]) {
      if (e.v != fa && !ban[e.id]) {
        single = false;
        break;
      }
    }
    ret = single;
  } else {
    std::vector<Candidate> candidates;
    find_candidate(u, fa, -1, fib[fib_id[size] - 1], fib[fib_id[size] - 2], candidates);
    candidates.pop_back();
    for (const Candidate& candidate : candidates) {
      ban[candidate.id] = true;
      bool ok =
        search(candidate.u, candidate.fa, candidate.size, candidate.is_full) &&
        search(candidate.fa, candidate.u, size - candidate.size, false);
      ban[candidate.id] = false;
      if (ok) {
        ret = true;
        break;
      }
    }
  }
  if (is_full) {
    f[u][fa] = ret;
  }
  return ret;
}

void dfs(int u, int fa) {
  parent[u] = fa;
  sz[u] = 1;
  for (const Edge& e : edges[u]) if (e.v != fa) {
    dfs(e.v, u);
    sz[u] += sz[e.v];
  }
}

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  std::istream& reader = std::cin;

  reader >> n;
  for (int i = 0; i < n - 1; ++i) {
    int x, y;
    reader >> x >> y; --x; --y;
    edges[x].emplace_back(Edge{.v = y, .id = i});
    edges[y].emplace_back(Edge{.v = x, .id = i});
  }

  while (fib.back() <= n) {
    fib.emplace_back(fib.back() + fib[(int)fib.size() - 2]);
  }
  fib.pop_back();
  DUMP(fib.size(), fib);
  m = fib.size();

  memset(fib_id, -1, sizeof(fib_id));
  for (int i = 1; i < m; ++i) {
    fib_id[fib[i]] = i;
  }

  dfs(0, -1);

  std::cout << (search(0, -1, n, true) ? "YES" : "NO")  << std::endl;
}