Farmer John's cows would like to host a dance party in their barn, complete with a laser light show. They plan to re-direct the laser light to the barn using a series of mirrors.

The layout of the farm has the laser at position (0,0) pointing north (positive y direction), and the barn at (Bx, By). There are already N cows (1 <= N <= 100,000) scattered throughout the farm holding mirrors aligned at angles of 45 degrees to the axes. For example, a mirror aligned like '\' will take a beam of light entering from below and reflect it to the left.

The laser cannot hit the barn with the mirrors in their current configuration. Bessie plans to hold up one more mirror (placed at a 45 degree angle) in order to redirect the laser onto the barn. Please count the number of locations in the field where Bessie can stand to accomplish this goal.

All coordinates are integers between -1,000,000,000 and 1,000,000,000. The beam should never come back to (0,0) after leaving. No two cows occupy the same point, and Bessie cannot locate herself at the same position as an existing cow.

Line 1: The integers N, Bx, and By.

Lines 2..N + 1: Line i+1 describes the ith mirror with 3 elements: its (x,y) location, and its orientation (either '\' or '/').

A single integer giving the number of locations where Bessie can stand to redirect the laser to the barn.

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출처 올림피아드 > USACO > 2013-2014 > US Open > Gold