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 namespace std;
unsigned int n;
bool correct = true;
vector<unsigned int> a, c, sub_size;
vector<vector<unsigned int>> g;
void calc_size(unsigned int ver) {
  sub_size[ver] = 1;
  for (unsigned int i = 0; i < g[ver].size(); ++i) {
    unsigned int child = g[ver][i];
    calc_size(child);
    sub_size[ver] += sub_size[child];
  }
}
void dfs(unsigned int ver, vector<unsigned int>& nums) {
  if (c[ver] >= nums.size()) correct = false;
  if (!correct) return;
  a[ver] = nums[c[ver]];
  for (unsigned int i = c[ver]; i < nums.size() - 1; ++i) {
    nums[i] = nums[i + 1];
  }
  nums.pop_back();
  vector<vector<unsigned int>> sub_nums(g[ver].size());
  unsigned int ind = 0;
  for (unsigned int i = 0; i < g[ver].size(); ++i) {
    unsigned int child = g[ver][i];
    for (unsigned int j = 0; j < sub_size[child]; ++j) {
      sub_nums[i].push_back(nums[ind]);
      ++ind;
    }
  }
  nums.clear();
  for (unsigned int i = 0; i < g[ver].size(); ++i) {
    unsigned int child = g[ver][i];
    dfs(child, sub_nums[i]);
    if (!correct) return;
  }
}
int main() {
  cin.tie();
  ios_base::sync_with_stdio(0);
  unsigned int n, p, root = 0;
  cin >> n;
  a.resize(n);
  c.resize(n);
  g.resize(n);
  sub_size.resize(n);
  for (unsigned int i = 0; i < n; ++i) {
    cin >> p;
    if (p != 0) {
      --p;
      g[p].push_back(i);
    } else {
      root = i;
    }
    cin >> c[i];
  }
  calc_size(root);
  vector<unsigned int> nums;
  for (unsigned int i = 1; i <= n; ++i) {
    nums.push_back(i);
  }
  dfs(root, nums);
  if (!correct) {
    cout << "NO";
  } else {
    cout << "YES\n";
    for (unsigned int i = 0; i < n; ++i) {
      cout << a[i] << " ";
    }
  }
  return 0;
}
