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>
using std::abs;
using std::array;
using std::cerr;
using std::cin;
using std::cout;
using std::generate;
using std::get;
using std::make_pair;
using std::make_tuple;
using std::map;
using std::max;
using std::max_element;
using std::min;
using std::min_element;
using std::pair;
using std::queue;
using std::reverse;
using std::set;
using std::sort;
using std::string;
using std::swap;
using std::tuple;
using std::unique;
using std::vector;
template <typename T>
T input() {
  T res;
  cin >> res;
  {};
  return res;
}
template <typename IT>
void input_seq(IT b, IT e) {
  std::generate(b, e,
                input<typename std::remove_reference<decltype(*b)>::type>);
}
int main() {
  std::iostream::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  int n = input<int>();
  vector<int> C(n);
  vector<vector<int>> graph(n);
  int root = -1;
  for (int i = 0; i < n; ++i) {
    int p;
    cin >> p >> C[i];
    --p;
    if (p == -1)
      root = i;
    else
      graph[p].push_back(i);
  }
  std::function<vector<int>(int)> dfs = [&](int v) {
    vector<int> rs;
    for (auto u : graph[v]) {
      auto ch = dfs(u);
      for (int elem : ch) rs.push_back(elem);
    }
    if (C[v] > int((rs).size())) {
      cout << "NO\n";
      exit(0);
    }
    rs.insert(rs.begin() + C[v], v);
    return rs;
  };
  auto rs = dfs(root);
  vector<int> x(n);
  for (int i = 0; i < n; ++i) x[rs[i]] = i + 1;
  cout << "YES\n";
  for (int i = 0; i < n; ++i) cout << x[i] << " \n"[i + 1 == n];
  return 0;
}
