Sign of a Product Without Multiplication

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given two signed 32-bit integers $a,b$, output whether their mathematical product is zero, positive, or negative. Do not multiply the values.

Input

One line contains signed integers $a,b$.

Output

Print ZERO for zero, POS for positive, or NEG for negative.

Subtasks

• Subtask 1 (20 points): Both integers are within [-10,10].

• Subtask 2 (30 points): Both integers are within [-100000,100000].

• Subtask 3 (50 points): Both are signed 32-bit integers.

Examples

Example 1

Input

-2147483648 -1

Output

POS

Explanation

For this input, the case-specific computation and the required exact output are shown above. Two negative nonzero factors have a positive product.

Example 2

Input

0 -5

Output

ZERO

Explanation

For this input, the case-specific computation and the required exact output are shown above. A zero factor makes the product zero.