5766: On Number of Decompositions into Multipliers
内存限制：256 MB
时间限制：2 S
题面：传统
评测方式：文本比较
上传者：
提交：2
通过：1
题目描述
A. On Number of Decompositions into Multipliers
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
You are given an integer m as a product of integers a1,a2,... an 
. Your task is to find the number of distinct decompositions of number m into the product of n ordered positive integers.
Decomposition into n products, given in the input, must also be considered in the answer. As the answer can be very large, print it modulo 1000000007 (109+7).
. Your task is to find the number of distinct decompositions of number m into the product of n ordered positive integers.
Decomposition into n products, given in the input, must also be considered in the answer. As the answer can be very large, print it modulo 1000000007 (109+7).
Input
The first line contains positive integer n (1≤n≤500). The second line contains space-separated integers a1,a2,...,an (1≤ai≤109).
Output
In a single line print a single number k − the number of distinct decompositions of number m into n ordered multipliers modulo 1000000007 (109+7).
Examples
Input
1 15
Output
1
Input
3 1 1 2
Output
3
Input
2 5 7
Output
4
Note
In the second sample, the get a decomposition of number 2, you need any one number out of three to equal 2, and the rest to equal 1.
In the third sample, the possible ways of decomposing into ordered multipliers are [7,5], [5,7], [1,35], [35,1].
A decomposition of positive integer m into n ordered multipliers is a cortege of positive integers b={b1,b2,... bn} such that
. Two decompositions b and c are considered different, if there exists index i such that bi≠ci.
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