It's the year \(3000\), and Bessie became the first cow in space! During her
journey between the stars, she found a number line with \(N\)
(\(2 \leq N \leq 5 \cdot 10^5\)) points, numbered from \(1\) to \(N\). All points are
initially colored white. She can perform the following operation any number of
times.

• Choose a position \(i\) within the number line and a positive integer \(x\). Then, color all the points in the interval \([i, i + x - 1]\) red and all points in \([i + x, i + 2x - 1]\) blue. All chosen intervals must be disjoint (i.e. no points in \([i, i + 2x - 1]\) can be already colored red or blue). The entire interval must also fall within the number line (i.e. \(1 \leq i \leq i + 2x - 1 \leq N\)).

Farmer John gives Bessie a string \(s\) of length \(N\) consisting of characters
\(R\), \(B\), and \(X\). The string represents Farmer John's color preferences for
each point: \(s_i=R\) means the \(i\)'th point must be colored red, \(s_i = B\) means
the \(i\)'th point must be colored blue, and \(s_i = X\) means there is no
constraint on the color for the \(i\)'th point.

Help Bessie count the number of distinct ways for the number line to be colored
while satisfying Farmer John's preferences. Two colorings are different if there
is at least one corresponding point with a different color. Because the answer
may be large, output it modulo \(10^9+7\).

Problem credits: Chongtian Ma, Alex Liang

SCORING

• Input 4: \(N\le 500\)
• Inputs 5-6: \(N\le 10^4\)
• Inputs 7-13: All but at most \(100\) characters in \(s\) are \(X\).
• Inputs 14-23: No additional constraints

Problem credits: Chongtian Ma, Alex Liang

The first line contains an integer \(N\).

The following line contains string \(s\).

Output the number of distinct ways for the number line to be colored while
satisfying Farmer John's preferences modulo
\(10^9+7\).

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