#include <bits/stdc++.h>
using namespace std;
const int N = 2000 + 1;
int n;
int c[N];
vector<int> g[N];
int a[N], sz[N];
void inc(int v, int x) {
  if (a[v] >= x) ++a[v];
  for (int u : g[v]) inc(u, x);
}
int dfs(int v, int t = 1) {
  a[v] = t + c[v];
  sz[v] = 1;
  int new_t = t;
  for (int u : g[v]) {
    t = dfs(u, t);
    inc(u, a[v]);
    sz[v] += sz[u];
  }
  if (sz[v] < c[v] + 1) {
    cout << "NO\n";
    exit(0);
  }
  return t + 1;
}
int main() {
  ios_base::sync_with_stdio(false);
  cout.tie(0);
  cin.tie(0);
  cin >> n;
  int root = -1;
  for (int i = 0; i < n; ++i) {
    int p;
    cin >> p >> c[i];
    if (p)
      g[p - 1].push_back(i);
    else
      root = i;
  }
  dfs(root);
  cout << "YES\n";
  for (int i = 0; i < n; ++i) cout << a[i] << ' ';
  cout << '\n';
}

### Prompt

Please provide a cpp coded solution to the problem described below:

Evlampiy was gifted a rooted tree. The vertices of the tree are numbered from 1 to n. Each of its vertices also has an integer a_i written on it. For each vertex i, Evlampiy calculated c_i — the number of vertices j in the subtree of vertex i, such that a_j < a_i. 

<image>Illustration for the second example, the first integer is a_i and the integer in parentheses is c_i

After the new year, Evlampiy could not remember what his gift was! He remembers the tree and the values of c_i, but he completely forgot which integers a_i were written on the vertices.

Help him to restore initial integers!

Input

The first line contains an integer n (1 ≤ n ≤ 2000) — the number of vertices in the tree.

The next n lines contain descriptions of vertices: the i-th line contains two integers p_i and c_i (0 ≤ p_i ≤ n; 0 ≤ c_i ≤ n-1), where p_i is the parent of vertex i or 0 if vertex i is root, and c_i is the number of vertices j in the subtree of vertex i, such that a_j < a_i.

It is guaranteed that the values of p_i describe a rooted tree with n vertices.

Output

If a solution exists, in the first line print "YES", and in the second line output n integers a_i (1 ≤ a_i ≤ {10}^{9}). If there are several solutions, output any of them. One can prove that if there is a solution, then there is also a solution in which all a_i are between 1 and 10^9.

If there are no solutions, print "NO".

Examples

Input


3
2 0
0 2
2 0


Output


YES
1 2 1 

Input


5
0 1
1 3
2 1
3 0
2 0


Output


YES
2 3 2 1 2

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int N = 2000 + 1;
int n;
int c[N];
vector<int> g[N];
int a[N], sz[N];
void inc(int v, int x) {
  if (a[v] >= x) ++a[v];
  for (int u : g[v]) inc(u, x);
}
int dfs(int v, int t = 1) {
  a[v] = t + c[v];
  sz[v] = 1;
  int new_t = t;
  for (int u : g[v]) {
    t = dfs(u, t);
    inc(u, a[v]);
    sz[v] += sz[u];
  }
  if (sz[v] < c[v] + 1) {
    cout << "NO\n";
    exit(0);
  }
  return t + 1;
}
int main() {
  ios_base::sync_with_stdio(false);
  cout.tie(0);
  cin.tie(0);
  cin >> n;
  int root = -1;
  for (int i = 0; i < n; ++i) {
    int p;
    cin >> p >> c[i];
    if (p)
      g[p - 1].push_back(i);
    else
      root = i;
  }
  dfs(root);
  cout << "YES\n";
  for (int i = 0; i < n; ++i) cout << a[i] << ' ';
  cout << '\n';
}

```