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Pyth, 22 bytes
J1ql{m+=Z*=J^.j)hCdzlz
Note the ASCII values of SRL, respectively 83, 76, 82. I abuse the fact that:
i 83 + 1 = 1
i 76 + 1 = i
i 82 + 1 = -i
From here I just keep a variable for the current position and current direction. For every character I multiply the current dire...