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Hi Guys,

Yesterday my nephew visited me and we played with lego.

We took board of 5 x 5 and created different mazes. We decided that we need perfect maze - One that has minimum lego pieces, but there should be exactly one path between each pair of cells without lego.

We quickly found out that we needed just 6 pieces and built all 22 configurations using them

Some of them:

But then he took his board of 13 x 13 and said - let's build perfect maze here!

Now we have no idea how many pieces we need and how many configurations we should build. Please help!

Output

Two numbers - number of single lego pieces we need to build perfect maze on 13x13 board and number of configurations of them.

Thanks!