#include <bits/stdc++.h>
using namespace std;
template <class T>
inline T mod_v(T num) {
  if (num >= 0)
    return num % 1000000007;
  else
    return (num % 1000000007 + 1000000007) % 1000000007;
}
template <class T>
inline T gcd(T a, T b) {
  a = abs(a);
  b = abs(b);
  while (b) b ^= a ^= b ^= a %= b;
  return a;
}
template <class T>
T fast_pow(T n, T p) {
  if (p == 0) return 1;
  if (p % 2) {
    T g = mod_v(mod_v(n) * mod_v(fast_pow(n, p - 1)));
    return g;
  } else {
    T g = fast_pow(n, p / 2);
    g = mod_v(mod_v(g) * mod_v(g));
    return g;
  }
}
template <class T>
inline T modInverse(T n) {
  return fast_pow(n, 1000000007 - 2);
}
bool equalTo(double a, double b) {
  if (fabs(a - b) <= 1e-9)
    return true;
  else
    return false;
}
bool notEqual(double a, double b) {
  if (fabs(a - b) > 1e-9)
    return true;
  else
    return false;
}
bool lessThan(double a, double b) {
  if (a + 1e-9 < b)
    return true;
  else
    return false;
}
bool lessThanEqual(double a, double b) {
  if (a < b + 1e-9)
    return true;
  else
    return false;
}
bool greaterThan(double a, double b) {
  if (a > b + 1e-9)
    return true;
  else
    return false;
}
bool greaterThanEqual(double a, double b) {
  if (a + 1e-9 > b)
    return true;
  else
    return false;
}
struct debugger {
  template <typename T>
  debugger& operator,(const T& v) {
    cerr << v << " ";
    return *this;
  }
} dbg;
int nextInt() {
  int n;
  scanf("%d", &n);
  return n;
}
long long nextLong() {
  long long n;
  scanf("%lld", &n);
  return n;
}
void print(int n) { printf("%d", n); }
void println(int n) { printf("%d\n", n); }
void println(long long n) { printf("%lld\n", n); }
template <class T>
inline int in(register T& num) {
  register char c = 0;
  num = 0;
  bool n = false;
  while (c < 33) c = getchar();
  while (c > 33) {
    if (c == '-')
      n = true;
    else
      num = num * 10 + c - '0';
    c = getchar();
  }
  num = n ? -num : num;
  return 1;
}
int par[1003];
vector<int> lst[1003];
int main() {
  int n, v;
  in(n);
  for (int i = 2; i <= n; i++) {
    in(v);
    par[v] = 1;
    lst[v].push_back(i);
  }
  bool ok = true;
  for (int i = 1; i <= n and ok; i++) {
    int cnt = 0;
    if (par[i]) {
      for (int j : lst[i]) {
        if (!par[j]) cnt++;
      }
      if (cnt < 3) ok = false;
    }
  }
  printf("%s", (ok == true ? "Yes" : "No"));
  return 0;
}

### Prompt

Please create a solution in Cpp 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;
template <class T>
inline T mod_v(T num) {
  if (num >= 0)
    return num % 1000000007;
  else
    return (num % 1000000007 + 1000000007) % 1000000007;
}
template <class T>
inline T gcd(T a, T b) {
  a = abs(a);
  b = abs(b);
  while (b) b ^= a ^= b ^= a %= b;
  return a;
}
template <class T>
T fast_pow(T n, T p) {
  if (p == 0) return 1;
  if (p % 2) {
    T g = mod_v(mod_v(n) * mod_v(fast_pow(n, p - 1)));
    return g;
  } else {
    T g = fast_pow(n, p / 2);
    g = mod_v(mod_v(g) * mod_v(g));
    return g;
  }
}
template <class T>
inline T modInverse(T n) {
  return fast_pow(n, 1000000007 - 2);
}
bool equalTo(double a, double b) {
  if (fabs(a - b) <= 1e-9)
    return true;
  else
    return false;
}
bool notEqual(double a, double b) {
  if (fabs(a - b) > 1e-9)
    return true;
  else
    return false;
}
bool lessThan(double a, double b) {
  if (a + 1e-9 < b)
    return true;
  else
    return false;
}
bool lessThanEqual(double a, double b) {
  if (a < b + 1e-9)
    return true;
  else
    return false;
}
bool greaterThan(double a, double b) {
  if (a > b + 1e-9)
    return true;
  else
    return false;
}
bool greaterThanEqual(double a, double b) {
  if (a + 1e-9 > b)
    return true;
  else
    return false;
}
struct debugger {
  template <typename T>
  debugger& operator,(const T& v) {
    cerr << v << " ";
    return *this;
  }
} dbg;
int nextInt() {
  int n;
  scanf("%d", &n);
  return n;
}
long long nextLong() {
  long long n;
  scanf("%lld", &n);
  return n;
}
void print(int n) { printf("%d", n); }
void println(int n) { printf("%d\n", n); }
void println(long long n) { printf("%lld\n", n); }
template <class T>
inline int in(register T& num) {
  register char c = 0;
  num = 0;
  bool n = false;
  while (c < 33) c = getchar();
  while (c > 33) {
    if (c == '-')
      n = true;
    else
      num = num * 10 + c - '0';
    c = getchar();
  }
  num = n ? -num : num;
  return 1;
}
int par[1003];
vector<int> lst[1003];
int main() {
  int n, v;
  in(n);
  for (int i = 2; i <= n; i++) {
    in(v);
    par[v] = 1;
    lst[v].push_back(i);
  }
  bool ok = true;
  for (int i = 1; i <= n and ok; i++) {
    int cnt = 0;
    if (par[i]) {
      for (int j : lst[i]) {
        if (!par[j]) cnt++;
      }
      if (cnt < 3) ok = false;
    }
  }
  printf("%s", (ok == true ? "Yes" : "No"));
  return 0;
}

```