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문제

Bobo has a lot of integers. Frankly, he has $a_1$ number of $1$, $a_2$ number of $2$, $\dots$, $a_{10}$ number of $10$.

Today, bobo would like to pick some of the numbers and calculate their product (If none of the numbers are chosen, the product is defined as $1$).  bobo is curious about the number of different products he can obtain, modulo $(10^9 + 7)$.

입력

$10$ integers $a_1, a_2, \dots, a_{10}$ ($0 \leq a_i \leq 10^9$).

출력

A single integer denotes the number of products.

예제 입력 1

0 1 0 1 0 0 0 1 0 0

예제 출력 1

7

예제 입력 2

0 1000000000 100000000 0 0 0 0 0 0 0

예제 출력 2

400000001