Problem Description

There are three piles of blocks arranged in a row, with each pile containing $a_1 \geq a_2 \geq a_3$ blocks.

In total, there are $N = a_1 + a_2 + a_3$ blocks, and we need to write integers from 1 to $N$ exactly once on these blocks.

However, all of the following conditions must be satisfied:

• Let $X_{i, j}$ denote the integer written on the $j$-th block from the bottom in the $i$-th pile from the left $(1 \leq i \leq 3, 1 \leq j \leq a_i)$, then
• $X_{i, j} > X_{i, j-1} (1 \leq i \leq 3, 1 < j \leq a_i)$
• $X_{i, j} > X_{i-1, j} (1 < i \leq 3, 1 \leq j \leq a_i)$

Find the number of ways to write the integers that satisfy these conditions.

Input Format

The input is given from the standard input in the following format:

$a_1$ $a_2$ $a_3$

Output Format

Output the number of ways to write the integers that satisfy the conditions.

Sample Input and Output

Sample Input #1

1 1 1

Sample Output #1

1

Sample Input #2

2 1 1

Sample Output #2

3

Sample Input #3

2 2 1

Sample Output #3

5

Notes/Hints

Constraints

• $3 \geq a_1 \geq a_2 \geq a_3 \geq 1$
• All inputs are integers.

Sample Explanation 1

There is only one way to write the numbers: 1, 2, 3 from left to right.

Sample Explanation 2

There are three possible ways to write the numbers as shown below:

见题面 Input 部分

见题面 Output 部分