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B. Christmas Spruce

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputConsider a rooted tree. A rooted tree has one special vertex called the root. All edges are directed from the root. Vertex *u* is called a child of vertex *v* and vertex *v* is called a parent of vertex *u* if there exists a directed edge from *v* to *u*. A vertex is called a leaf if it doesn't have children and has a parent.

Let's call a rooted tree a spruce if its every non-leaf vertex has at least 3 leaf children. You are given a rooted tree, check whether it's a spruce.

The definition of a rooted tree can be found here.

Input

The first line contains one integer *n* — the number of vertices in the tree (3 ≤ *n* ≤ 1 000). Each of the next *n* - 1 lines contains one integer *p*_{i} (1 ≤ *i* ≤ *n* - 1) — the index of the parent of the *i* + 1-th vertex (1 ≤ *p*_{i} ≤ *i*).

Vertex 1 is the root. It's guaranteed that the root has at least 2 children.

Output

Print "Yes" if the tree is a spruce and "No" otherwise.

Examples

Input

4

1

1

1

Output

Yes

Input

7

1

1

1

2

2

2

Output

No

Input

8

1

1

1

1

3

3

3

Output

Yes

Note

The first example:

The second example:

It is not a spruce, because the non-leaf vertex 1 has only 2 leaf children.

The third example:

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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