Lexicographic String Comparison

Version: Phuoc Hung OJ Extended

Problem Statement

Given two strings $a$ and $b$, compare them using Python 3 lexicographic order. Scan from left to right; at the first differing position, the string with the smaller Unicode code point comes first. If the common prefix is identical, the shorter string comes first. Identical strings are equal.

Report whether $a<b$, $a=b$, and $a>b$, in that order. Comparisons are case-sensitive and preserve Vietnamese characters.

Input

The first line contains $a$; the second contains $b$. Either string may be empty.

Output

Print three lines corresponding to $a<b$, $a=b$, and $a>b$. Each line is exactly True or False.

Subtasks

• Subtask 1 (100 points): $0\le |a|,|b|\le50$ Unicode characters.

Examples

Example 1

Input

An
Binh

Output

True
False
False

Explanation. At the first position, A precedes B, so only $a<b$ is True.

Example 2

Input

A
A

Output

False
True
False

Explanation. Both strings equal A, so only equality evaluates to True.

Example 3

Input

abc
ab

Output

False
False
True

Explanation. ab is a prefix of abc; the longer string follows it, so $a>b$.