Problem Statement

Takahashi is the administrator of a network consisting of N computers and 1 central server. The N computers are numbered from 1 to N, and the central server is numbered as computer 0. That is, the entire network consists of a total of N + 1 computers: computers 0, 1, \ldots, N.

Each computer i (1 \leq i \leq N) is directly connected to a parent computer P_i (0 \leq P_i \leq N, P_i \neq i). These connections form a tree structure with N + 1 vertices rooted at the central server (computer 0). In this tree structure, a child computer of computer v refers to a computer j satisfying P_j = v.

One day, a virus infiltrated the network. Each computer i (1 \leq i \leq N) has a vulnerability value D_i assigned to it.

Virus infection targets only computers 1 through N. The central server (computer 0) is not subject to infection and will never become infected. Infection spreads in a chain reaction according to the following rules:

1. Initial infection: All computers with a positive vulnerability value (D_i > 0) become infected. Computers with a vulnerability value of 0 or less (D_i \leq 0) are not infected at this stage. However, they may become infected later through Rule 2 below.

1. Propagation of infection (child → parent direction): For a computer v (1 \leq v \leq N) that is not yet infected, let a be the number of infected child computers of v, and b be the number of non-infected child computers of v. If a > b is satisfied, then v becomes newly infected. This determination is made regardless of the vulnerability value D_v of computer v itself. That is, even if D_v \leq 0, v becomes infected if the condition on the infection status of its child computers is met. Note that for a computer with no child computers, a = b = 0, which does not satisfy a > b, so such a computer will not become infected by this rule. Infection only occurs in the direction where a parent becomes infected based on the infection status of its children. Even if a parent computer becomes infected, this does not cause its child computers to become newly infected.

1. Repetition: The determination and infection in Rule 2 are repeated until no new computers become infected in a round. The determination in each round is performed simultaneously for all computers based on the infection status at the beginning of that round. That is, if multiple computers become newly infected in a given round, they all become infected simultaneously, and the infection status does not change partway through the same round. The determination in the next round is based on the updated infection status.

Determine the total number of computers that are ultimately infected. The central server (computer 0) is not subject to infection and should not be included in the count.

Constraints

• 1 \leq N \leq 2 \times 10^5
• 0 \leq P_i \leq N, P_i \neq i (1 \leq i \leq N)
• The given connections form a tree structure with N + 1 vertices rooted at computer 0
• -10^9 \leq D_i \leq 10^9 (1 \leq i \leq N)
• All input values are integers

Sample Input 1

6
0 -1
1 1
1 2
1 0
2 -5
3 0

Sample Output 1

3

Sample Input 2

4
0 0
0 -3
0 -1
0 0

Sample Output 2

0

Sample Input 3

15
0 -5
1 -1
1 -1
1 0
2 1
2 1
2 0
3 -1
3 2
3 0
4 1
4 0
8 1
8 1
8 0

Sample Output 3

10

Sample Input 4

40
0 -100
1 0
1 -1
1 -1
2 -1
2 -1
2 3
3 -2
3 -2
3 -2
4 1
4 0
4 1
5 0
5 1
5 1
6 -1
6 2
7 0
7 -5
8 1
8 0
8 1
9 -1
9 -1
10 1
10 1
10 0
17 1
17 0
17 1
19 1
19 0
20 -1
20 -1
24 1
24 1
25 0
25 1
34 1

Sample Output 4

28

Sample Input 5

1
0 -1000000000

Sample Output 5

0