Drunk Coding

It is the night before the ACM-ICPC contest. To unwind, Sanggeun heads to a nearby bar with his teammates.

To warm up for the next day's contest, they decide to play a small game.

First, Seonyeong writes down a sequence of $N$ integers $X_1, X_2, \dots, X_N$ for Sanggeun. The game consists of $K$ rounds, and in each round Seonyeong issues one of the following two commands.

• Change: Replace one value of the sequence with a new value.
• Multiply: Seonyeong names $i$ and $j$; Sanggeun must answer whether the product $X_i \times X_{i+1} \times \dots \times X_j$ is positive, negative, or zero.

Every wrong answer to a multiply command costs Sanggeun a shot of soju. Luckily, Seonyeong lets him use his laptop, and Sanggeun trusts his coding skills more than his mental arithmetic.

Write a program that helps Sanggeun answer each multiply command.

The input consists of several test cases, processed one after another until end of file.

The first line of each test case contains the sequence size $N$ and the number of rounds $K$. ($1 \le N, K \le 10^5$)

The second line contains the values $X_1, X_2, \dots, X_N$ separated by spaces. ($-100 \le X_i \le 100$)

Each of the next $K$ lines contains one command, starting with the letter C or P.

• C i V: a change command; set $X_i$ to $V$. ($1 \le i \le N$, $-100 \le V \le 100$)
• P i j: a multiply command; ask for the sign of $X_i \times \dots \times X_j$. ($1 \le i \le j \le N$)

Each test case contains at least one multiply command.

For each test case, print the results of all its multiply commands concatenated on a single line. The $i$-th character is the result of the $i$-th multiply command: print + if the product is positive, - if it is negative, and 0 if it is zero.

Ballmer's Peak Theory is the (tongue-in-cheek) claim that programmers write superhuman code when their blood alcohol concentration is between 0.129% and 0.138%.