Problem: 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](https://goo.gl/1dqvzz).

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:

<image>

The second example:

<image>

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

The third example:

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int inf = 0x3f3f3f3f;
int intcmp(const void *v1, const void *v2) { return *(int *)v1 - *(int *)v2; }
inline int read() {
  int x = 0, f = 1;
  char cc = getchar();
  while (cc < '0' || cc > '9') {
    if (cc == '-') f = -1;
    cc = getchar();
  }
  while (cc >= '0' && cc <= '9') {
    x = x * 10 + cc - '0';
    cc = getchar();
  }
  return x * f;
}
const int maxn = 20010;
int a[maxn];
int vis[maxn];
int main() {
  int i;
  int n;
  n = read();
  memset(vis, 0, sizeof(vis));
  for (i = 2; i <= n; i++) {
    a[i] = read();
    vis[a[i]] = 1;
  }
  for (i = n; i >= 1; i--) {
    if (vis[i] == 0) {
      vis[a[i]]++;
    }
  }
  for (i = 1; i <= n; i++) {
    if (vis[i] && vis[i] < 4) break;
  }
  if (i > n) {
    puts("Yes");
  } else {
    puts("No");
  }
  return 0;
}