Exact and Approximate Sum Comparison

Version: Phuoc Hung OJ Extended

Problem Statement

Given four real numbers $a$, $b$, $c$ and $target$, compute $s=(a+b)+c$ as Python float, in left-to-right evaluation order. Report the result of exact equality s == target and then the default approximate comparison math.isclose(s, target). The two answers may differ.

Input

The only line contains four real numbers $a$, $b$, $c$ and $target$, in that order.

Output

Print exactly two lines: the True/False result of s == target on line 1 and of math.isclose(s, target) on line 2.

Subtasks

• Subtask 1 (100 points): All four inputs are finite.

Examples

Example 1

Input

0.1 0.1 0.1 0.3

Output

False
True

Explanation. Left-to-right floating-point addition gives s = 0.30000000000000004. Exact comparison with 0.3 yields False; the default approximate comparison yields True.

Example 2

Input

0.5 0.5 0.5 1.5

Output

True
True

Explanation. Left-to-right floating-point addition gives s = 1.5. Exact comparison with 1.5 yields True; the default approximate comparison yields True.

Example 3

Input

0.2 0.2 0.2 0.6

Output

False
True

Explanation. Left-to-right floating-point addition gives s = 0.6000000000000001. Exact comparison with 0.6 yields False; the default approximate comparison yields True.