Quadrant

Source: beecrowd

Version: Phuoc Hung OJ Extended

Problem Statement

Read integer coordinate pairs in order. For pairs with both coordinates nonzero, print the quadrant: I (+,+), II (-,+), III (-,-), IV (+,-). Stop at the first pair with x=0 or y=0, without printing for that pair.

Input

Each line contains an integer pair x,y; a terminating pair has x=0 or y=0.

Output

One line per nonterminating point: primeiro, segundo, terceiro or quarto for quadrants I–IV.

Subtasks

• Subtask 1 (20%): The first pair is terminating.
• Subtask 2 (30%): At most 10 nonterminating points; coordinate magnitude <= 10.
• Subtask 3 (50%): At most 1000 nonterminating points; coordinate magnitude <= 1000000.

Examples

Example 1

Input

2 2
3 -2
-8 -1
-7 1
0 2

Output

primeiro
quarto
terceiro
segundo

Explanation

The four nonzero pairs belong to quadrants I, IV, III and II, respectively. The pair (0,2) terminates input.

Example 2

Input

0 0

Output

Explanation

The first pair is the sentinel, so output is empty.