Problem B
Varied Amusements

Marika and Lisa love going to amusement parks. This time, they have their eyes set on a park with lots of exciting rides of three different types: tilt-a-whirls, roller coasters and drop towers. There are $a$ different tilt-a-whirls, $b$ roller coasters and $c$ drop towers. They want to ride $n$ rides in sequence, but never two rides of the same type in a row. In how many ways can they choose such sequences of $n$ rides?

Input

The first and only line of input contains the integers $n$ ($1\le n\le 50$), $a$ ($1\le a\le 50$), $b$ ($1\le b\le 50$) and $c$ ($1\le c\le 50$) as described in the problem statement.

Output

Output the number of valid amusement ride sequences. Since this number can be very large, output it modulo ${10}^9+7$.

Scoring

Your solution will be tested on a set of test groups, each worth a number of points. To get the points for a test group you need to solve all test cases in the test group.

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