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>

typedef long long ll;

using namespace std;


struct Node {
    ll id = 0;
    ll size = 0;
    bool visited = false;
    vector<pair<Node *, ll>> adj;
    ll counted = 0;
    Node *n;
};

bool check(vector<Node> *nodes, ll nodeSize) {
    if (nodeSize == 1)
        return true;
    for (ll i = 0; i < nodeSize; ++i) {
        (*nodes)[i].visited = false;
    }
    ll a = 1, b = 1;
    while (b < nodeSize) {
        ll temp = b;
        b += a;
        a = temp;
    }
    if (b != nodeSize) return false;

    for (ll i = 0; i < nodeSize; ++i) {
        if ((*nodes)[i].counted == (*nodes)[i].adj.size() - 1) {
            Node *curNode = &(*nodes)[i];

            while (curNode->counted == curNode->adj.size() - 1) {
                curNode->size++;
                curNode->visited = true;
                curNode->counted++;
                for (auto &next : curNode->adj) {
                    if (!next.first->visited) {
                        next.first->size += curNode->size;
                        next.second = curNode->size;
                        next.first->counted++;
                        curNode = next.first;
                        break;
                    }
                }
            }
        }
    }

    bool stop = false;
    for (ll i = 0; i < nodeSize; ++i) {
        for (ll j = 0; j < (*nodes)[i].adj.size(); ++j) {
            if ((*nodes)[i].adj[j].second == a || (*nodes)[i].adj[j].second == b - a) {
                for (ll k = 0; k < (*nodes)[i].adj[j].first->adj.size(); ++k) {
                    if ((*nodes)[i].adj[j].first->adj[k].first == &(*nodes)[i]) {
                        (*nodes)[i].adj[j].first->adj.erase((*nodes)[i].adj[j].first->adj.begin() + k);
                    }
                }
                (*nodes)[i].adj.erase((*nodes)[i].adj.begin() + j);
                stop = true;
                break;
            }
        }
        if (stop) break;
    }
    if (!stop) return false;
    for (ll i = 0; i < nodeSize; ++i) {
        (*nodes)[i].visited = false;
        (*nodes)[i].size = 0;
        (*nodes)[i].counted = 0;
    }
    vector<Node> nodes1(a), nodes2(a);

    stack<Node *> stack;
    stack.push(&(*nodes)[0]);

    ll pos = 0;
    while (!stack.empty()) {
        Node *s = stack.top();
        stack.pop();

        if (!(*s).visited) {
            nodes1[pos] = (*s);
            (*s).n = &nodes1[pos];
            pos++;
            (*s).visited = true;
        }

        for (auto i = (*s).adj.begin(); i != (*s).adj.end(); ++i)
            if (!i->first->visited)
                stack.push((i->first));
    }

    ll nodes1Size = a;
    if (pos < a){
        nodes1Size = b - a;
    }
    pos = 0;
    for (ll i = 0; i < nodeSize; ++i) {
        if (!(*nodes)[i].visited) {
            stack.push(&(*nodes)[i]);

            while (!stack.empty()) {
                Node *s = stack.top();
                stack.pop();

                if (!(*s).visited) {
                    nodes2[pos] = (*s);
                    (*s).n = &nodes2[pos];
                    pos++;
                    (*s).visited = true;
                }

                for (auto i = (*s).adj.begin(); i != (*s).adj.end(); ++i)
                    if (!i->first->visited)
                        stack.push((i->first));
            }
            break;
        }
    }

    for (ll i = 0; i < nodes1Size; ++i) {
        for (ll j = 0; j < nodes1[i].adj.size(); ++j) {
            nodes1[i].adj[j].first = nodes1[i].adj[j].first->n;
        }
    }

    for (ll i = 0; i < b - nodes1Size; ++i) {
        for (ll j = 0; j < nodes2[i].adj.size(); ++j) {
            nodes2[i].adj[j].first = nodes2[i].adj[j].first->n;
        }
    }

    return check(&nodes1, nodes1Size) && check(&nodes2, b - nodes1Size);
}

int main() {
#ifdef _DEBUG
    freopen("input.txt", "r", stdin);
//	freopen("output.txt", "w", stdout);
#endif
    ios::sync_with_stdio(false);
    cin.tie(0);
    ll n;
    cin >> n;

    vector<Node> nodes(n);
    for (ll i = 0; i < n; ++i) {
        nodes[i].id = i;
    }
    for (ll i = 0; i < n - 1; ++i) {
        ll x, y;
        cin >> x >> y;
        nodes[x - 1].adj.emplace_back(make_pair(&nodes[y - 1], 0));
        nodes[y - 1].adj.emplace_back(make_pair(&nodes[x - 1], 0));
    }

    if (check(&nodes, nodes.size())) cout << "YES" << endl;
    else cout << "NO" << endl;

    return 0;
}