Hello 2018-B. Christmas Spruce

B. Christmas Spruce

time limit per test
1 second

memory limit per test
256 megabytes

input
standard input

output
standard output

Consider 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 pi (1 ≤ i ≤ n - 1) —
the index of the parent of the i + 1-th vertex (1 ≤ pi ≤ 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:



一道简单题，直接遍历两遍即可。

Code：

#include<bits/stdc++.h>
#define N 1005
using namespace std;
int a
,f
,sum
;
int main()
{
int n;
scanf("%d",&n);
for(int i=2;i<=n;i++)
{
scanf("%d",&a[i]);
sum[a[i]]++;
}
for(int i=2;i<=n;i++)
if(!sum[i])f[a[i]]++;
for(int i=1;i<=n;i++)
if(sum[i]&&f[i]<3)
{
puts("No");
return 0;
}
puts("Yes");
return 0;
}