E. Fib-tree
time limit per test: 1 second
memory limit per test: 256 megabytes
input: standard input
output: standard output
Let Fk denote the k-th term of Fibonacci sequence, defined as below:
- F0=F1=1
- for any integer n≥0, Fn+2=Fn+1+Fn
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 Fk 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 Fk 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).