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Problems

Jackpots

Jackpots

Time limit 1 second
Memory limit 128 MiB

The rules of the final round of King's Lottery in Byteland are simple:

  • The player starts to draw balls from an opaque bag containing a red balls, b green balls and c blue balls initially.

  • After the player draws the ball, the ball is not returned into the bag.

  • The player continues the process until he collects all a red balls, or all b green balls, or all c blue balls.

  • The player wins the Gold Jackpot if he collects a red balls, Silver Jackpot if he collects b green balls, or Bronze Jackpot otherwise.

Given a, b and c, calculate the probabilities of winning each jackpot.

Input data

Contains three integers a, b and c~(1 \le a, b, c \le 1000).

Output data

Print three irreducible fractions p_G, p_S and p_B denoting the probability of winning the Gold Jackpot, the Silver Jackpot and the Bronze Jackpot, respectively. The fractions shall be printed in the form p / q.

Examples

Input example #1
1 1 1
Output example #1
1/3 1/3 1/3
Input example #2
1 2 3
Output example #2
7/12 4/15 3/20
Source 2022 Azerbaijan ICPC Qualification