A Lockheed Martin F-22 Raptor has gone on a mission to bomb an old military hideout . Three bombs are dropped in succession at it .

The probabilities of a hit in the first shot is \( \frac{1}{2} \) , in the second is \( \frac{2}{3} \) and in the third is \( \frac{3}{4} \) .

In case of one hit , the probability of destroying the target is \( \frac{2}{3} \) , in case of two hits is \( \frac{7}{11} \) and in case of three hits is \( 1 \) .

Find the probability of destroying the hideout in three shots .

The answer is of the form \( \frac{f}{g} \) where \( f \) and \( g \) are co-prime numbers ;

Report the last three digits of \( f^{g} \) .

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