In ICPCCamp, there are only three capitals -- Alpha, Beta and Gamma. There are also $a$ bidirectional roads between capitals Alpha and Beta, $b$ roads between Alpha and Gamma, and $c$ roads between Beta and Gamma.

Bobo lives in capital Alpha and would like to travel around ICPCCamp. He will start from capital Alpha, travel along each road exactly once, and return back to capital Alpha.

It is clear that Bobo has many plans to choose from. He would like to find out the number of different plans, modulo $(10^9+7)$.

Note that two plans $A$ and $B$ are considered different only if there exists an $i$ where the $i$-th traveled road in plan $A$ is different from the $i$-th road in plan $B$.

Input

The input contains at most $30$ sets. For each set:

The first line contains $3$ integers $a, b, c$ ($1 \leq a, b, c \leq 10^5$).

Output

For each set, an integer denotes the number of different ways modulo $(10^9+7)$.

Sample Input

1 1 3
1 3 1
100000 100000 100000

Sample Output

12
24
525502296