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#!/usr/bin/env python
# -*- coding: utf-8 -*-
def find_paths(n, pos=(0, 0), path=''):
directions = {'R': (0, 1), 'L': (1, 0), 'H': (1, 1)}
paths = []
if pos == (n-1, n-1):
return [path]
for move, (dx, dy) in directions.items():
new_pos = (pos[0]+dx, pos[1]+dy)
if 0 <= new_pos[0] < n and pos[1] <= new_pos[1] < n:
paths.extend(find_paths(n, new_pos, path+move))
return paths
# For N = 1
print(find_paths(2))
# For N = 2
print(find_paths(3))
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