Problem Statement

You were told that you play games too much, and your parent has set a password on your game. Moreover, your parent is cautious: letting $X$ be the game's password, they split it into $N$ integers whose sum is $X$, and entrusted each of them to a separate server.
You want to play the game, so you tried to somehow find the password. You managed to gain access to the servers, but you can only send strange queries.
The queries are as follows. Let $a_i$ be the number stored on the $i\ (1\leq i \leq N)\ $-th server. Also, $b_i\ (1 \leq i \leq N)\ $ initially have the value $0$.
Query $1$: Send an integer $j\ (1 \leq j \leq N)\ $. For each $b_i\ (1 \leq i \leq N)\ $, add the value $a_j^i$ and replace it with the result modulo $998244353$.
Query $2$: Send a permutation $\ P=(p_1,p_2,...,p_N)\ $ of $(1,2,...,N)\ $. For each $b_j\ (1 \leq j \leq N)\ $, add $\ \sum_{i=1}^{N} a_{p_i}j^{i-1}\ $ and replace it with the result modulo $998244353$.
Query $3$: Send integers $i,j\ (1 \leq i,j \leq N)\ $. Replace both $b_i$ and $b_j$ with $\ b_ib_j\ $ modulo $998244353$.
Query $4$: Send integers $i,x\ (1 \leq i \leq N,1 \leq x \leq 998244352)\ $. Replace $b_i$ with $\ b_ix\ $ modulo $998244353$.
Query $5$: Send integers $i,x\ (1 \leq i \leq N,1 \leq x \leq 998244352)\ $. Replace $b_i$ with $\ b_i+x\ $ modulo $998244353$.
You can send up to $1000$ queries in total. After all queries are finished, you are told only the value of $\ \sum_{i=1}^{N}b_i\ $ modulo $998244353$.
By asking your parent, you learned that $N=30\ $. Using this, perform operations so that $\sum_{i=1}^{N}a_i=(\sum_{i=1}^{N}b_i) \mod 998244353\ $ holds, and get the password.

Input

No input is given.
$a_i(1 \leq i \leq N)$ satisfy the following conditions.
・$0 \leq a_i \leq 10^7$
・$a_i$ are fixed by the judge before it reads the queries

Output

$M
\\query_1
\\query_2
\\ \ldots
\\query_M$

Letting $M$ be the number of queries, output in the format above. Here, $1 \leq M \leq 1000$ must hold.
Also, output each $query_i(1 \leq i \leq M)$ in one of the following forms.

$1
\\j$

$2
\\p_1 \ p_2 \ ... \ p_N$

$3
\\i \ j$

$4
\\i\  x$

$5
\\i \ x$

Sample

5
1
3
2
1 3 2
3
1 2
4
1 5
5
1 1000