**Time limit:**1.00 s**Memory limit:**512 MB

- the number of divisors is $6$ (they are $1$, $2$, $3$, $4$, $6$, $12$)

- the sum of divisors is $1+2+3+4+6+12=28$

- the product of divisors is $1 \cdot 2 \cdot 3 \cdot 4 \cdot 6 \cdot 12 = 1728$

**Input**

The first line has an integer $n$: the number of parts in the prime factorization.

After this, there are $n$ lines that describe the factorization. Each line has two numbers $x$ and $k$ where $x$ is a prime and $k$ is its power.

**Output**

Print three integers modulo $10^9+7$: the number, sum and product of the divisors.

**Constraints**

- $1 \le n \le 10^5$

- $2 \le x \le 10^6$

- each $x$ is a distinct prime

- $1 \le k \le 10^9$

**Example**

Input:

`2`

2 2

3 1

Output:

`6 28 1728`