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
#include <bits/stdc++.h>
const int MAX_N = 2000;
std::vector<int> list[MAX_N + 3];
int d[MAX_N + 3];
int c[MAX_N + 3];
int p[MAX_N + 3];
int root;
int res[MAX_N + 3];
int n;
int size[MAX_N + 3];
void input() {
  std::cin >> n;
  for (int i = 1; i <= n; i++) {
    std::cin >> p[i] >> c[i];
    list[p[i]].push_back(i);
    if (p[i] == 0) root = i;
  }
}
void dfs1(int v, int f) {
  size[v] = 1;
  for (auto u : list[v]) {
    if (u != f) {
      d[u] = d[v] + 1;
      dfs1(u, v);
      size[v] += size[u];
    }
  }
}
void solve() {
  input();
  dfs1(root, -1);
  for (int i = 1; i <= n; i++) {
    if (c[i] > size[i] - 1) {
      std::cout << "NO\n";
      return;
    }
  }
  std::set<std::pair<int, int> > set;
  int done = 0;
  for (int i = 1; i <= n; i++)
    if (c[i] == 0) set.insert(std::make_pair(d[i], i));
  int next = 1;
  while (!set.empty()) {
    int v = (*set.begin()).second;
    set.erase(set.begin());
    res[v] = next++;
    int it = p[v];
    while (it > 0) {
      c[it]--;
      if (c[it] == 0) set.insert(std::make_pair(d[it], it));
      it = p[it];
    }
  }
  std::cout << "YES\n";
  for (int i = 1; i <= n; i++) std::cout << res[i] << " ";
  std::cout << "\n";
}
int main() {
  std::ios_base::sync_with_stdio(0);
  std::cin.tie(NULL);
  solve();
}
