Problem Statement

You are given an integer sequence $A=(A_1,A_2,\cdots,A_N)$ of length N, and another integer sequence $P=(P_2,\cdots,P_N)$ of length N-1. Note that the index of P starts at 2. It is guaranteed that $1 \leq P_i < i$ for each i.
You will now repeat the following operation 10^{100} times.

• For each $i=2,\cdots,N$, in this order, replace the value of A_{P_i} with A_{P_i}+A_{i}.

Determine whether A_1 will be positive, negative, or zero when all operations are completed.

Input

The input is given from Standard Input in the following format:
N
$A_1 A_2 \cdots A_N$
$P_2 \cdots P_N$

Output

If A_1 is positive when all operations are completed, print +; if it is negative, print -; if it is zero, print 0.

Constraints

• $2 \leq N \leq 250000$
• -$10^9 \leq A_i \leq 10^9$
• $1 \leq P_i < i$
• All input values are integers.

Sample Input 1

4
1 -2 3 -4
1 2 3

Sample Output 1

-

Shown below are the results of the first few operations.

• After the first operation:
• Before the operation: A=(1,-2,3,-4).
• Processing for i=2: Replace the value of A_1 with A_1+A_2=1+(-2)=-1.
• Processing for i=3: Replace the value of A_2 with A_2+A_3=-2+3=1.
• Processing for i=4: Replace the value of A_3 with A_3+A_4=3+(-4)=-1.

• After the operation: A=(-1,1,-1,-4).

• After the second operation, A=(0,0,-5,-4).

• After the third operation, A=(0,-5,-9,-4).
• After the fourth operation, A=(-5,-14,-13,-4).
• $\vdots$

After 10^{100} operations, A_1 will be negative.
Thus, you should print -.

Sample Input 2

3
0 1 -1
1 1

Sample Output 2

0

Sample Input 3

5
1 -1 1 -1 1
1 1 2 2

Sample Output 3

+

Sample Input 4

20
568273618 939017124 -32990462 -906026662 403558381 -811698210 56805591 0 436005733 -303345804 96409976 179069924 0 0 0 -626752087 569946496 0 0 0
1 1 1 4 4 6 7 2 2 3 3 8 13 14 9 9 15 18 19

Sample Output 4

+

见题面 Input 部分

见题面 Output 部分