# Two pegs on a square

**Geometry**Level 4

A unit square \(ABCD\) has two points \(M,N\) inside it (possible on the perimeter) such that \(\overline{MA} + \overline{MB} + \overline{MC} + \overline{NA} + \overline{ND} + \overline{NC} \) is a minimum.

If \( \overline{MN} = \frac {\sqrt a }{b} \), then what is the value of \(a+b\)?