The edge length of a regular tetrahedron $ABCD$ is $2.$ $M$ and $N$ are the midpoints of $\overline{BC}$ and $\overline{AD}$, respectively. Find $MN.$ [asy] size(150); import three; currentprojection = orthographic(-0.6,3,2); triple A,B,C,D,O,M,NN; O=(0,0,0);read more .. 
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