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;
using namespace std;
int rt, n, fa[2005], c[2005], sz[2005], a[2005];
vector<int> g[2005], num;
inline void dfs1(int u) {
  int v;
  sz[u] = 1;
  for (int i = 0; i < g[u].size(); ++i) {
    v = g[u][i];
    dfs1(v);
    sz[u] += sz[v];
  }
}
inline bool dfs2(int u, const vector<int> &num) {
  int v, p = 0;
  if (c[u] >= sz[u]) return 1;
  a[u] = num[c[u]];
  vector<int> sb;
  for (int i = 0; i < g[u].size(); ++i) {
    v = g[u][i];
    sb.clear();
    while (sb.size() < sz[v]) {
      if (p != c[u]) {
        sb.push_back(num[p]);
      }
      ++p;
    }
    if (dfs2(v, sb)) return 1;
  }
  return 0;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) {
    scanf("%d%d", fa + i, c + i);
    if (fa[i])
      g[fa[i]].push_back(i);
    else
      rt = i;
    num.push_back(i);
  }
  dfs1(rt);
  if (dfs2(rt, num)) {
    puts("NO");
    return 0;
  }
  puts("YES");
  for (int i = 1; i <= n; ++i) {
    printf("%d ", a[i]);
  }
  puts("");
  return 0;
}
