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

n = int(input())
sz = {}
a = {}
vis = {}
c = {}
g = [[]for i in range(n+10)]
flag = 1

for i in range(1, n+1):
    x, y = map(int, input().split())
    c[i]= y
    g[x].append(i)

def dfs(u):
    global flag
    if u>0:
        sum = 0
        for i in range(1, n+1):
            if i not in vis:
                sum += 1
            if sum == c[u] + 1:
                a[u] = i
                vis[i] = 1
                break
    sz[u] = 1
    for i in range(len(g[u])):
        dfs(g[u][i])
        sz[u] += sz[g[u][i]]
    if u>0 and sz[u]-1 < c[u]:
        flag = 0
    return

dfs(0)

if flag==0:
    print("No")
else:
    print("Yes")
    for i in range(1, 1+n):
        print(a[i], end=' ')
   		 		 				  		   	  	 				