J, 43 36 bytes
[:#(#~0{]>://&.|:@/:{:"1)^:(1<#)^:a:
Uses greedy algorithm. Probably more to golf....
orig brute force, 43 bytes
[:>./(2#:@i.@^#)(#*;-:~.@;)@#<@([+i.@-~)/"1
Jonah
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