E. Become Big For Me
time limit per test
3 seconds
memory limit per test
512 megabytes
standard input
standard output
Come, let's build a world where even the weak are not forgotten!
—Kijin Seija, Double Dealing Characters

Shinmyoumaru has a mallet that can turn objects bigger or smaller. She is testing it out on a sequence $$$a$$$ and a number $$$v$$$ whose initial value is $$$1$$$. She wants to make $$$v = \gcd\limits_{i\ne j}\{a_i\cdot a_j\}$$$ by no more than $$$10^5$$$ operations ($$$\gcd\limits_{i\ne j}\{a_i\cdot a_j\}$$$ denotes the $$$\gcd$$$ of all products of two distinct elements of the sequence $$$a$$$).

In each operation, she picks a subsequence $$$b$$$ of $$$a$$$, and does one of the followings:

  • Enlarge: $$$v = v \cdot \mathrm{lcm}(b)$$$
  • Reduce: $$$v = \frac{v}{\mathrm{lcm}(b)}$$$

Note that she does not need to guarantee that $$$v$$$ is an integer, that is, $$$v$$$ does not need to be a multiple of $$$\mathrm{lcm}(b)$$$ when performing Reduce.

Moreover, she wants to guarantee that the total length of $$$b$$$ chosen over the operations does not exceed $$$10^6$$$. Fine a possible operation sequence for her. You don't need to minimize anything.


The first line contains a single integer $$$n$$$ ($$$2\leq n\leq 10^5$$$) — the size of sequence $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1,a_2,\cdots,a_n$$$ ($$$1\leq a_i\leq 10^6$$$) — the sequence $$$a$$$.

It can be shown that the answer exists.


The first line contains a non-negative integer $$$k$$$ ($$$0\leq k\leq 10^5$$$) — the number of operations.

The following $$$k$$$ lines contains several integers. For each line, the first two integers $$$f$$$ ($$$f\in\{0,1\}$$$) and $$$p$$$ ($$$1\le p\le n$$$) stand for the option you choose ($$$0$$$ for Enlarge and $$$1$$$ for Reduce) and the length of $$$b$$$. The other $$$p$$$ integers of the line $$$i_1,i_2,\ldots,i_p$$$ ($$$1\le i_1<i_2<\ldots<i_p\le n$$$) represents the indexes of the subsequence. Formally, $$$b_j=a_{i_j}$$$.

6 10 15
0 3 1 2 3
2 4 8 16
0 1 4
1 1 1

Test case 1:

$$$\gcd\limits_{i\ne j}\{a_i\cdot a_j\}=\gcd\{60,90,150\}=30$$$.

Perform $$$v = v\cdot \operatorname{lcm}\{a_1,a_2,a_3\}=30$$$.

Test case 2:

$$$\gcd\limits_{i\ne j}\{a_i\cdot a_j\}=8$$$.

Perform $$$v = v\cdot \operatorname{lcm}\{a_4\}=16$$$.

Perform $$$v = \frac{v}{\operatorname{lcm}\{a_1\}}=8$$$.