G++ Language

The genius Kyojun spent several years of research and built a new programming language, G++. G++ supports the following operations:

• "INPUT $x$": Reads one integer from the input and writes it to memory $x$. If there are no more integers to read, an Input Error occurs.
• "NOT $x$ $y$": Writes the logical negation of the value in memory $x$ to memory $y$.
• "BNOT $x$ $y$": Writes the bitwise NOT of the value in memory $x$ to memory $y$.
• "AND $n$ $x\_1$ … $x\_n$ $y$": Writes the bitwise AND of the $n$ values in memories $x\_1$ … $x\_n$ to memory $y$. $x\_1$, …, $x\_n$ must all be different, and $n≥2$. If this is not satisfied, an Index Error occurs.
• "OR $n$ $x\_1$ … $x\_n$ $y$": Writes the bitwise OR of the $n$ values in memories $x\_1$ … $x\_n$ to memory $y$. $x\_1$, …, $x\_n$ must all be different, and $n≥2$. If this is not satisfied, an Index Error occurs.
• "XOR $n$ $x\_1$ … $x\_n$ $y$": Writes the bitwise XOR of the $n$ values in memories $x\_1$ … $x\_n$ to memory $y$. $x\_1$, …, $x\_n$ must all be different, and $n≥2$. If this is not satisfied, an Index Error occurs.
• "LSHIFT $x\_1$ $x\_2$ $y$": Writes the value in memory $x\_1$ shifted left bitwise by the value in memory $x\_2$ to memory $y$.
• "RSHIFT $x\_1$ $x\_2$ $y$": Writes the value in memory $x\_1$ shifted right bitwise by the value in memory $x\_2$ to memory $y$.

A G++ program runs its operations in order, starting from the first. Right when it starts, memory is allocated for $10^3$ int variables. If your code accesses memory $x$, then $0≤x<10^3$ must hold. Otherwise, a Memory Error occurs. At the start, all $10^3$ variables are initialized to $0$.

The total number of operations in a G++ program must not exceed $10^5$. Otherwise, a Time Limit Exceeded Error occurs.

The total number of memory accesses in a G++ program must not exceed $10^5$. Otherwise, an Access Limit Exceeded Error occurs.

Kyojun is a perfectionist. Your G++ code must not contain unnecessary spaces or line breaks. The last character of the G++ code must be a newline character. Otherwise, a Compile Error occurs.

In addition, if your G++ code causes Undefined Behavior, a Runtime Error occurs. The following cases cause Undefined Behavior when a G++ program runs:

• When shifting $x$ left by $y$ bits, $y≥0$ and $x × 2^y < 2^{31}$ must both hold. Also, if $x<0$, then $y=0$ must hold. Otherwise, Undefined Behavior occurs.
• When shifting $x$ right by $y$ bits, if $y≥0$ does not hold, Undefined Behavior occurs.

For the input "2 16 5", the following G++ code writes the value 5 to memory 4.

INPUT 2
NOT 2 3
NOT 3 2
INPUT 0
INPUT 0
XOR 3 0 1 2 1
OR 3 3 1 2 4

You must now solve the following problem in G++:

There is a two-dimensional grid of size $H×W$, with $W$ cells wide and $H$ cells tall. The top-left cell has coordinates $(0, 0)$, and the bottom-right cell has coordinates $(H-1, W-1)$. The cell at coordinates $(i, j)$ contains the number $A_{i×W+j}$.

Consider a rectangle in the grid whose top-left corner is $(a, b)$ and whose bottom-right corner is $(c, d)$. Let $S$ be the sum of the numbers in the cells inside this rectangle. You must write a G++ code that, for the following input, leaves $S$ in memory 0 after running, and leaves $0$ in every other memory.

The input given to the G++ program is as follows:

$H$ $W$ $A_0$ $A_1$ … $A_{H×W-1}$ $a$ $b$ $c$ $d$

You are given only two integers, $H$ and $W$. In other words, your submitted code can read only the values of $H$ and $W$. Note that the values of $A_0$, …, $A_{H×W-1}$, $a$, $b$, $c$, and $d$ are not provided.

After running, memory 0 must contain $S$, and every other memory must contain $0$. Print the G++ code.

All data satisfy the following conditions:

• $H$, $W$, $A_0$, …, $A_{H×W-1}$ are all positive integers.
• $H×W≤16$.
• For every integer $i$ with $0 ≤ i < H×W$, $A_i ≤ 100$.
• $a$, $b$, $c$, $d$ are all integers.
• $0 ≤ a ≤ c < H$, $0 ≤ b ≤ d < W$.