We define a bitset as a $w$-bit $01$ string. The bitset representation of a $w\times w$ $01$ matrix $M$ is defined as a sequence of $w$ bitsets $b_1, \ldots, b_w$, where $b_i$ is the bitset corresponding to the $i$-th row of $M$, with the element in the $j$-th column occupying the $j$-th bit of the bitset.

Given the bitset representation of a $w\times w$ matrix $M$ stored in $b_1, \ldots, b_w$ (you cannot directly access their values), you need to find the bitset representation of its transpose $M^T$ and store the result in $b_1, \ldots, b_w$. You have a total of $10^5$ bitsets $b_1, \ldots, b_{10^5}$ available, where $b_{w+1}, \ldots, b_{10^5}$ are initially all zeros. You can perform the following operations:

• AS x y: Set $b_x \leftarrow b_y$.
• AND x y z: Set $b_x \leftarrow b_y \land b_z$, where $\land$ is the bitwise AND.
• OR x y z: Set $b_x \leftarrow b_y \lor b_z$, where $\lor$ is the bitwise OR.
• XOR x y z: Set $b_x \leftarrow b_y \oplus b_z$, where $\oplus$ is the bitwise XOR.
• SET x y a v: Set $b_x$ to the result of modifying the $a$-th bit ($a \in [0, w)$) of $b_y$ to $v$ ($v \in \{0, 1\}$) (without changing $b_y$).
• SH x y a: Set $b_x$ to the result of left-shifting $b_y$ by $a$ bits ($a \in (-w, w)$) (without changing $b_y$; if $a < 0$, it is a right shift by $-a$ bits, with $0$s filled in the vacated positions).
• SUB x s y: Set $b_x \leftarrow b_{s+b_y}$, where $b_y$ is treated as a binary number. It is required that $-10^5 \leq s \leq 10^5$ and $1 \leq s+b_y \leq 10^5$.

Your score depends on the number of operations you perform; see the scoring section for details.

Input

Read from standard input.

The first line contains an integer $w$.

Output

Output to standard output.

The first line contains an integer $m$, representing the number of operations.

The next $m$ lines each represent an operation. Operations will be executed in the order they are output.

Examples

Input

2

Output

10
SET 3 3 0 1
SET 4 4 1 1
AND 5 1 3
AND 6 1 4
AND 7 2 3
AND 8 2 4
SH 9 6 -1
SH 10 7 1
OR 1 5 10
OR 2 8 9

Subtasks

$\text{Subtask 1}(5\%)$: $w=2$.

$\text{Subtask 2}(10\%)$: $w=128$.

$\text{Subtask 3}(36\%)$: $w=256$.

$\text{Subtask 4}(49\%)$: $w=1024$.

Scoring

Let $m$ be the number of operations you perform.

Your score on a test case is: if your output is incorrect, the score is $0$; otherwise, the score is $f(m)$. Your score on a subtask is the minimum of the scores obtained on all test cases within that subtask.

For $\text{Subtask 1}$, $f(m)=[m\leq 10^5]\times 5$.

For $\text{Subtask 2}$, $f(m)=[m\leq 10^5]\times 10$.

For $\text{Subtask 3}$, $f(m)=\begin{cases}0 & (m>262144)\\\dfrac{8}{3}\left(4-\dfrac{m}{65536}\right)^2 & (65536< m\leq 262144)\\ 36-\dfrac{64}{3}\left(\dfrac{m}{65536}-\dfrac{1}{4}\right)^2 & (16384 < m\leq 65536)\\ 36 & (m\leq 16384)\end{cases}$

• This is a continuous function. For reference, $f(65536)=24$.

For $\text{Subtask 4}$, $f(m)=\begin{cases}0 & (m>80000)\\\dfrac{3}{4000}(80000-m) & (40000 < m\leq 80000)\\ 48-\dfrac{9}{2282}(m-35436) & (35435< m\leq 40000)\\ 49 & (m\leq 35435)\end{cases}$

• This is a continuous function on $(35435, +\infty)$. For reference, $f(40000)=30, f(35436)=48$.