998244353 → 1000000007

**This problem is output-only.** We have a programming language equipped with the following operations of unsigned 64-bit integers: addition, multiplication, and a modulo operation where the divisor is $998244353$. Write a program that performs multiplication modulo $1000000007$ in this language. More formally, write a program that receives integers $a$ and $b$ between $0$ and $1000000006$ and computes $a \times b \bmod{1000000007}$ under the following **Specification** and **Format**. ## Input The input given from Standard Input is empty. ## Format The $1$\-st line of the program contains an integer $N$ $(1 \leq N \leq 100)$ representing the number of instructions in the program. The $2$\-nd through $(N + 1)$\-th lines contain $N$ instructions. The instructions are executed one by one from top to bottom. Each instruction is in one of the following three forms. * `add x y z` * Assign $(y + z) \bmod{2^{64}}$ to $x$, where $x$ is a variable, and each of $y$ and $z$ is a variable or an unsigned 64-bit integer. * `mul x y z` * Assign $(y \times z) \bmod{2^{64}}$ to $x$, where $x$ is a variable, and each of $y$ and $z$ is a variable or an unsigned 64-bit integer. * `rem x y` * Assign $y \bmod{998244353}$ to $x$, where $x$ is a variable, and $y$ is a variable or an unsigned 64-bit integer. ## Specification The program can handle $26$ **variables** represented by uppercase English letters: $A, B, \dots, Z$. Each variable can hold an integer value between $0$ and $2^{64}-1$ (inclusive). Below, such a value is called **unsigned 64-bit integer**. At the start of the execution of the program, $A$ is assigned an integer $a$, $B$ is assigned an integer $b$, and the other variables are assigned $0$. At the end of the execution, $C$ must hold $a \times b \bmod{1000000007}$. [samples]