Once upon a time, there was an n-dimensional space. And there was a planet, quite a strange planet. One of its strange features was its form — n-dimensional hypercube with unit length side. And there was a strange town in each vertex of the planet. Territory of the planet was divided between three aggressive kingdoms. But several towns preserved their independence — let's call them neutral. An i-th town was neutral if d₁(i)=d₂(i)=d₃(i), where d_j(i) is the distance between i-th town and the capital of j-th kingdom. All distances are measured using Manhattan metrics, because the planet was really strange. You should calculate amount of neutral towns in order to estimate trading potential of the planet. Answer can be quite big, so output it modulo 10⁹+7.
First three lines describe the positions of the capitals. Each description is an n-bit string ().
You should output the amount of the neutral towns modulo 10⁹+7.

sample input	sample output
01 01 10	2

sample input	sample output
01 01 11	0