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A recent result shows that 2FRP in directed graphs can be solved in $\\tilde{O}(n^3)$ time [arXiv:2209.07016]. In this paper, we show a 3FRP algorithm in deterministic $\\tilde{O}(n^3)$ time for undirected weighted graphs, which almost matches the size of the output. This implies that $f$FRP in undirected graphs can be solved in almost optimal $\\tilde{O}(n^f)$ time for all $f\\geq 3$. 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