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Finally solved this problem after a lot of efforts. Approach:
With F# (so .NET), this approach solves all test cases but the last one. With java, this exact same approach solves all test cases (test case 9 takes 3 seconds).
I'm disappointed to see that all my efforts to solve this problem in F# have failed. I see that some people managed to solve this problem with C#, so it could be that another approach than mine would be fast enough also in F#.