Dice Roll Sum

Background

In a casual board game, players roll two six-sided dice to determine their actions. To add more fun to the game, sometimes special rules are introduced.

Problem Description

Given the values of two 6-sided dice rolls, each in the range $1$ to $6$. Return their sum. However, if noDoubles is true, and the two dice show the same value, increment one die to the next value, wrapping around to $1$ if its value was $6$.

Input Format

Input is given from standard input in the following format.

die1 die2 noDoubles

die1 and die2 are the values of the two dice, and noDoubles is a boolean value (true or false).

Output Format

Output is printed to standard output in the following format.

sum

The adjusted sum of the two dice rolls.

Sample

2 3 true

5

3 3 true

7

3 3 false

6

Sample Explanation

• Sample 1: Dice values are $2$ and $3$. Since they are not doubles, the noDoubles rule does not apply. The sum is $2 + 3 = 5$.
• Sample 2: Both dice values are $3$. Since they are doubles and noDoubles is true, we increment one die's value from $3$ to $4$. The sum is $3 + 4 = 7$.
• Sample 3: Both dice values are $3$. Although they are doubles, noDoubles is false, so the special rule is not applied. The sum is $3 + 3 = 6$.

Constraints

• $1 \le ext{die1}, ext{die2} \le 6$
• noDoubles is true or false.
• Time limit: 1 second
• Memory limit: 1024 KB