Mint Choco

Interview

Time limit1sMemory limit1024 MB

Summary

Given a chain of integer multiplications and divisions, decide whether the overall value is an integer or a non-integer rational.

Level: Medium5 of 10
Topics: Math, Number theory, Hash map, Implementation
Solved: No attempts yet

Problem

Sangwon picks his dessert in a very unusual way.

Sangwon writes an arbitrary expression made up only of multiplications and divisions of integers. If the result is an integer, he eats "mint choco"; if the result is a rational number that is not an integer, he eats "toothpaste".

Given the expression Sangwon wrote, determine which dessert he will eat.

Input

The first line gives $N$ , the number of numbers in the expression. ( $1 \leq N \leq 100\ 000$ )

The second line gives the expression. The expression consists of integers and operators (*, /) separated by spaces. Integers and operators alternate, and the expression always starts and ends with an integer. Every integer in the expression is between $-100\ 000$ and $100\ 000$ , inclusive.

Only valid expressions are given, and no case divides by $0$ .

Output

If the dessert Sangwon picked is "mint choco", print mint chocolate; if it is "toothpaste", print toothpaste.

Examples2

Example 1
Input
```
6
1 * 2 / 3 / 4 * 5 * 6
```
Expected output
```
mint chocolate
```
Example 2
Input
```
6
1 * 2 / 3 / 4 / 5 * 6
```
Expected output
```
toothpaste
```