7.2 Odd or Even

Score: 60pts

Time Limit: 1.00 sec

Rohan’s teacher instructed the class to divide themselves into two teams, team Odd and team Even. She gave the class a number \(n\) and told them to calculate the product of the lowest common multiple of all odd or even numbers from 1 to \(n\) - 1 and \(n\). The people that used odd numbers will be placed in team Odd and those that used even numbers will be placed in team Even. The team with the larger product will not have any homework that day. Help Rohan decide which team he should be a part of so that he doesn’t have to do his homework.

Constraints

\(1 \leq n \leq 100\)

Input Format

The first and only line contains an integer \(n\).

Output Format

On the first line print ‘ODD’ if he should be in team Odd and print ‘EVEN’ if he should be in team Even.

On the next line print the total product calculated by team Odd and team Even separated by a space

(Print the product as modulo \(10^{9} + 7\) as the product can be large)

On the next line print the total product calculated by team Odd and team Even separated by a space

(Print the product as modulo \(10^{9} + 7\) as the product can be large)

Example 1

Input:

5

Output:

EVEN

75 200

Explanation:

The odd numbers from 1 to 4 are 1 and 3 so the product would be LCM(1, 5) * LCM(3, 5) = 5 * 15 = 75

The even numbers from 1 to 4 are 2 and 4 so the product would be LCM(2, 5) * LCM(4, 5) = 10 * 20 = 200

5

Output:

EVEN

75 200

Explanation:

The odd numbers from 1 to 4 are 1 and 3 so the product would be LCM(1, 5) * LCM(3, 5) = 5 * 15 = 75

The even numbers from 1 to 4 are 2 and 4 so the product would be LCM(2, 5) * LCM(4, 5) = 10 * 20 = 200

Example 2

Input:

6

Output:

ODD

1080 72

Explanation:

The odd numbers from 1 to 5 are 1, 3 and 5 so the product would be LCM(1, 6) * LCM(3, 6) * LCM(5, 6) = 6 * 6 * 30 = 1080

The even numbers from 1 to 5 are 2 and 4 so the product would be LCM(2, 6) * LCM(4, 6) = 6 * 12 = 72

6

Output:

ODD

1080 72

Explanation:

The odd numbers from 1 to 5 are 1, 3 and 5 so the product would be LCM(1, 6) * LCM(3, 6) * LCM(5, 6) = 6 * 6 * 30 = 1080

The even numbers from 1 to 5 are 2 and 4 so the product would be LCM(2, 6) * LCM(4, 6) = 6 * 12 = 72