#include <bits/stdc++.h>
using namespace std;
const long double EPS = 1e-10;
const long long int MOD = 1000000007ll;
const long long int mod1 = 1000000009ll;
const long long int mod2 = 1100000009ll;
int INF = (int)1e9;
long long int INFINF = (long long int)1e18;
int debug = 0;
long long int bit_count(long long int _x) {
  long long int _ret = 0;
  while (_x) {
    if (_x % 2 == 1) _ret++;
    _x /= 2;
  }
  return _ret;
}
long long int power(long long int _a, long long int _b) {
  long long int _r = 1;
  while (_b) {
    if (_b % 2 == 1) _r = (_r * _a);
    _b /= 2;
    _a = (_a * _a);
  }
  return _r;
}
long long int add(long long int a, long long int b, long long int m = MOD) {
  long long int x = (a % m + b % m) % m;
  return x;
}
long long int sub(long long int a, long long int b, long long int m = MOD) {
  long long int x = a - b;
  while (x < 0) x += m;
  return x;
}
long long int mul(long long int a, long long int b, long long int m = MOD) {
  long long int x = a * b;
  x %= m;
  return x;
}
long long int powermod(long long int _a, long long int _b,
                       long long int _m = MOD) {
  long long int _r = 1;
  while (_b) {
    if (_b % 2 == 1) _r = (_r * _a) % _m;
    _b /= 2;
    _a = (_a * _a) % _m;
  }
  return _r;
}
long long int invmod(long long int a, long long int m = MOD) {
  return powermod(a, m - 2, m);
}
long long int gcd(long long int a, long long int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long int lcm(long long int a, long long int b) {
  return (a * b) / gcd(a, b);
}
const int N = (1e6) + 5;
const int M = (2e5) + 5;
const int LN = 20;
const int sz = 32000;
const int B = 32;
const int BB = (1e9 + sz - 1) / sz;
int dx[] = {-1, 1, 0, 0};
int dy[] = {0, 0, -1, 1};
int n;
vector<int> g[1001];
bool chk() {
  for (int i = 1; i <= n; i++) {
    int cnt = 0;
    if (g[i].size() == 0) continue;
    for (auto v : g[i]) {
      if (g[v].size() == 0) cnt++;
    }
    if (cnt < 3) return false;
  }
  return true;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n - 1; i++) {
    int p;
    scanf("%d", &p);
    g[p].push_back(i + 1);
  }
  puts(chk() ? "Yes" : "No");
  return 0;
}

### Prompt

Your task is to create a Cpp solution to the following 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>

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const long double EPS = 1e-10;
const long long int MOD = 1000000007ll;
const long long int mod1 = 1000000009ll;
const long long int mod2 = 1100000009ll;
int INF = (int)1e9;
long long int INFINF = (long long int)1e18;
int debug = 0;
long long int bit_count(long long int _x) {
  long long int _ret = 0;
  while (_x) {
    if (_x % 2 == 1) _ret++;
    _x /= 2;
  }
  return _ret;
}
long long int power(long long int _a, long long int _b) {
  long long int _r = 1;
  while (_b) {
    if (_b % 2 == 1) _r = (_r * _a);
    _b /= 2;
    _a = (_a * _a);
  }
  return _r;
}
long long int add(long long int a, long long int b, long long int m = MOD) {
  long long int x = (a % m + b % m) % m;
  return x;
}
long long int sub(long long int a, long long int b, long long int m = MOD) {
  long long int x = a - b;
  while (x < 0) x += m;
  return x;
}
long long int mul(long long int a, long long int b, long long int m = MOD) {
  long long int x = a * b;
  x %= m;
  return x;
}
long long int powermod(long long int _a, long long int _b,
                       long long int _m = MOD) {
  long long int _r = 1;
  while (_b) {
    if (_b % 2 == 1) _r = (_r * _a) % _m;
    _b /= 2;
    _a = (_a * _a) % _m;
  }
  return _r;
}
long long int invmod(long long int a, long long int m = MOD) {
  return powermod(a, m - 2, m);
}
long long int gcd(long long int a, long long int b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long int lcm(long long int a, long long int b) {
  return (a * b) / gcd(a, b);
}
const int N = (1e6) + 5;
const int M = (2e5) + 5;
const int LN = 20;
const int sz = 32000;
const int B = 32;
const int BB = (1e9 + sz - 1) / sz;
int dx[] = {-1, 1, 0, 0};
int dy[] = {0, 0, -1, 1};
int n;
vector<int> g[1001];
bool chk() {
  for (int i = 1; i <= n; i++) {
    int cnt = 0;
    if (g[i].size() == 0) continue;
    for (auto v : g[i]) {
      if (g[v].size() == 0) cnt++;
    }
    if (cnt < 3) return false;
  }
  return true;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n - 1; i++) {
    int p;
    scanf("%d", &p);
    g[p].push_back(i + 1);
  }
  puts(chk() ? "Yes" : "No");
  return 0;
}

```