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
mod = 1000000007
eps = 10**-9


def main():
    import sys
    from collections import deque
    input = sys.stdin.readline

    N = int(input())
    par = [0] * (N+1)
    child = [[] for _ in range(N+1)]
    C = [0] * (N+1)
    for v in range(1, N+1):
        p, c = map(int, input().split())
        par[v] = p
        C[v] = c
        child[p].append(v)
        if p == 0:
            root = v

    que = deque()
    que.append(root)
    seq = []
    while que:
        v = que.popleft()
        seq.append(v)
        for u in child[v]:
            que.append(u)
    seq.reverse()
    size = [1] * (N+1)
    for v in seq:
        for u in child[v]:
            size[v] += size[u]

    order = [[] for _ in range(N+1)]
    for v in seq:
        if C[v] > size[v] - 1:
            print("NO")
            exit()
        for u in child[v]:
            order[v].extend(order[u])
        order[v].insert(C[v], v)

    print("YES")
    ans = [0] * N
    for i, v in enumerate(order[root]):
        ans[v-1] = i+1
    print(*ans)


if __name__ == '__main__':
    main()
