#include <bits/stdc++.h>
using namespace std;
const int maxn = 2000 + 7;
const int mod = 1e9 + 7;
const long long INF = 9223372036854775807;
const int inf = 2e9 + 7;
vector<int> g[maxn];
int c[maxn];
int res[maxn];
int n;
vector<int> dfs(int now) {
  vector<int> res;
  for (int x : g[now]) {
    vector<int> ch = dfs(x);
    for (int v : ch) {
      res.push_back(v);
    }
  }
  if (c[now] > res.size()) {
    cout << "NO" << endl;
    exit(0);
  }
  res.insert(res.begin() + c[now], now);
  return res;
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    int fa;
    cin >> fa;
    cin >> c[i];
    g[fa].push_back(i);
  }
  vector<int> ans = dfs(0);
  for (int i = 0; i < (int)ans.size(); i++) {
    res[ans[i]] = i;
  }
  cout << "YES" << endl;
  for (int i = 1; i <= n; i++) {
    cout << res[i] << ' ';
  }
  cout << endl;
  return 0;
}

### Prompt

Your challenge is to write a cpp solution to the following problem:

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 maxn = 2000 + 7;
const int mod = 1e9 + 7;
const long long INF = 9223372036854775807;
const int inf = 2e9 + 7;
vector<int> g[maxn];
int c[maxn];
int res[maxn];
int n;
vector<int> dfs(int now) {
  vector<int> res;
  for (int x : g[now]) {
    vector<int> ch = dfs(x);
    for (int v : ch) {
      res.push_back(v);
    }
  }
  if (c[now] > res.size()) {
    cout << "NO" << endl;
    exit(0);
  }
  res.insert(res.begin() + c[now], now);
  return res;
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    int fa;
    cin >> fa;
    cin >> c[i];
    g[fa].push_back(i);
  }
  vector<int> ans = dfs(0);
  for (int i = 0; i < (int)ans.size(); i++) {
    res[ans[i]] = i;
  }
  cout << "YES" << endl;
  for (int i = 1; i <= n; i++) {
    cout << res[i] << ' ';
  }
  cout << endl;
  return 0;
}

```