Problem Statement

Suppose there is a bit sequence $a[0], a[1], \cdots, a[N]$ of length $N+1$ ($a[i] \in \{0, 1\}$). The initial values of the first $N$ elements are $B[0], B[1], \cdots, B[N-1]$ (these are not revealed to you), and the initial value of the remaining element is $0$. Your goal is to finally make $a[N]$ the following value.

• If at least $K$ of $B[0], B[1], \cdots, B[N-1]$ are $1$, then $a[N] = 1$
• Otherwise, $a[N] = 0$

• UPD i x: Set $a[i] = x$.
• AND i j k: Set $a[i] = a[j] \ \rm{AND}$$\ a[k]$.
• XOR i j k: Set $a[i] = a[j] \ \rm{XOR}$$\ a[k]$.

Input

$N$ $K$
$T$
$C_{1,0}$ $C_{1,1}$ $C_{1,2}$ $\cdots$ $C_{1,N-1}$
$C_{2,0}$ $C_{2,1}$ $C_{2,2}$ $\cdots$ $C_{2,N-1}$
$\vdots$
$C_{T,0}$ $C_{T,1}$ $C_{T,2}$ $\cdots$ $C_{T,N-1}$

$T$ is the number of test cases, and $C_{i, j}$ is the value of $B[j]$ in the $i$-th test case.

Output

On line $1$, output the number of operations to perform. Then, output the operations to perform, each in one of the formats UPD i x, AND i j k, or XOR i j k.

Constraints

• $2 \leq N \leq 50$
• $1 \leq K \leq N$
• $1 \leq T \leq 100$
• $C_{i, j} \in \{0, 1\}$
• All inputs are integers

Sample

2 1
3
0 0
0 1
1 1

2
UPD 2 0
XOR 2 1 2