Zero Number and Nonempty String

Version: Phuoc Hung OJ Extended

Problem Statement

A text string $s$ represents a valid decimal integer; it may have a + or - sign and leading zero digits. Distinguish these three values:

• Boolean value of the string: True if it is nonempty.
• Boolean value of the represented integer: False only if the value is $0$.
• Original text length, counting an optional sign and every leading zero.

Do not remove leading zeros before determining the text length.

Input

One line contains $s$: an optional + or - sign followed by at least one ASCII digit, with no spaces.

Output

Print three lines: the string's Boolean value, the integer's Boolean value, and the original string length. Use exactly True or False for Boolean values.

Subtasks

• Subtask 1 (100 points): $1\le |s|\le15$; $|\operatorname{int}(s)|\le10^9$.

Examples

Example 1

Input

0

Output

True
False
1

Explanation. Text 0 is nonempty and therefore True; the integer zero is False; text length is $1$.

Example 2

Input

000

Output

True
False
3

Explanation. 000 is nonempty text of length $3$ but represents integer zero.

Example 3

Input

-12

Output

True
True
3

Explanation. -12 is nonempty and nonzero; both Boolean values are True, and its sign counts toward length $3$.