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;
struct compare {
  bool operator()(const int64_t &a, const int64_t &b) { return a > b; }
};
bool customS(pair<int, int> a, pair<int, int> b) {
  if (a.first == b.first) return a.second < b.second;
  return a.first < b.first;
}
bool customS2(pair<int64_t, int64_t> a, pair<int64_t, int64_t> b) {
  return (a.first) < (b.first);
}
class CompareDist {
 public:
  bool operator()(pair<int64_t, int64_t> a, pair<int64_t, int64_t> b) {
    return a.first < b.first;
  }
};
int64_t gcd(int64_t a, int64_t b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
double gcdfloat(double a, double b) {
  if (a < b) return gcd(b, a);
  if (fabs(b) < 0.001)
    return a;
  else
    return (gcd(b, a - floor(a / b) * b));
}
vector<vector<int64_t> > nodes(1001);
vector<int64_t> visited(1001, 0);
int DFS(int64_t start, bool *ans) {
  visited[start] = 1;
  if (nodes[start].size() == 0) return 1;
  int64_t ctr = 0;
  for (int i = 0; i < nodes[start].size(); i++) {
    if (visited[nodes[start][i]] == 0) {
      int temp = DFS(nodes[start][i], ans);
      if (temp == 1) ctr++;
    }
  }
  if (ctr < 3) {
    *ans = false;
  }
  return 0;
}
int64_t LCA(int64_t a, int64_t b) {
  while (a != b) {
    if (b > a) {
      swap(a, b);
    }
    a /= 2;
  }
  return a;
}
map<int64_t, int64_t> hash1;
bool check(int c, int d) {
  string a = to_string(c), b = to_string(d);
  int i;
  for (i = 0; i < a.length(); i++) {
    if (a[i] == '7') return true;
  }
  for (i = 0; i < b.length(); i++) {
    if (b[i] == '7') return true;
  }
  return false;
}
vector<int64_t> ra(int64_t n) {
  vector<int64_t> arr(n);
  for (int i = 0; i < n; i++) cin >> arr[i];
  return arr;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int64_t i, j, a = 0, b = 0, c = 0, d = 0, n, m, k, sum = 0, x = 0, y = 0,
                z = 0, flag = 0, zero = 0, ans = 0;
  string s, newS;
  cin >> n;
  for (i = 1; i <= (n - 1); i++) {
    cin >> a;
    nodes[a].push_back(i + 1);
  }
  bool result = true;
  DFS(1, &result);
  if (result == true)
    cout << "Yes\n";
  else
    cout << "No\n";
  return 0;
}