Hard-working Student

Billy is a hard-working student. He is fond of computers and wants to learn as much as possible about them. He is currently studying graph theory and must write a program to construct the graph shown in the figure above.

The vertices of the graph are labeled sequentially with integer keys from $0$ to N-1 (N \leq 10000). There are two types of edges: backward edges, labeled with $\mathbf{B}$ in the figure (for example, from node $4$ to node $2$, or from node $3$ to node $1$), and forward edges, labeled with $\mathbf{F}$ (for example, from node $1$ to node $2$, or from node $0$ to node $3$).

Billy's program initially works with a graph that contains the vertices $0$, $1$, $2$, and $3$. Then, it should build the graph according to a sequence of commands given in a text file. Each command has the following format:

$index0$ $string\_of\_characters$ $index1$

where $index0$ and $index1$ are the numbers of the vertices, and $string\_of\_characters$ is a sequence of operations to be performed from right to left. An operation is represented by one of the following characters:

Here, $\mathbf{v}$ is the array of graph vertices. The argument of the first operation is the vertex $v[index1]$. The result of the $f$ and $b$ operations is a vertex, which becomes the argument for all the remaining operations. The $<$ and $=$ operations must appear on the leftmost position. As an example, consider the following command:

index0 = 4, index1 = 0

x = f(v[0]) // forward to node 3, x = 3 y = f(x) // forward creates node (4), y = 4 k(y) // prints the key (4) V[4] = y // put node (4) in array v

A vertex is put into the array $v$ only by the $<$ operation. Initially, $v$ contains the vertices with keys $0$, $1$, $2$, $3$: v[0]=0, v[1]=1, v[2]=2, v[3]=3.

Examples

An input/output sample is shown in the table below.

Example 1

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