Printed-Circuit Boards

The company Bytel has started producing series-parallel electronic circuits. Every such circuit is made of electronic units, of connections between the units, and of two power connections. A series-parallel circuit is one of the following:

• a single unit;

• several smaller series-parallel circuits joined in series;

• two branching units that join several smaller series-parallel circuits in parallel.

The circuits are mounted on two-sided printed-circuit boards, so every connection runs either on the top side or on the bottom side of the board. To keep manufacturing cheap, as many connections as possible should run on the bottom side; however, every unit must have at least one connection reaching it from the top side.

Write a program that:

• reads the description of a series-parallel circuit,
• computes the minimum number of connections that must run on the top side of the board,
• prints that number.

The input contains the description of one series-parallel circuit, given in a recursive form:

• a line S n, where $2 \le n \le 10000$, means the circuit consists of $n$ smaller circuits joined in series; their descriptions follow on the next lines;
• a line R n, where $2 \le n \le 10000$, means the circuit consists of $n$ smaller circuits joined in parallel (through two branching units); their descriptions follow on the next lines;
• a line containing a single letter X describes a circuit made of exactly one unit.

The total number of X letters in the description does not exceed $10^7$, and the nesting depth of the description does not exceed $500$.

Print a single integer: the minimum number of connections that must run on the top side of the board.