J, 75 72 71 70 68 bytes
+/@,@;@((-:&(/:~)"#.(,{@;~0 _1)&{&>)#])&,[:g@|:&>g=.[:;@,<@(1}.<\)\.
alternate approach, 72 bytes
+/@,@;@(((-:&(/:~)&,({@;~0 _1)&{)&>~<)#&,[)~[:g@|:&>g=.a:-.~[:,(1}.<\)\.
Jonah
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