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.

Constraints

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

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.