# Derek's permutations

Let $$N$$ be the number of permutations $$\tau$$ of $$(1,4,9,16,25,36,49)$$ such that

$\tau(1) + \tau(9) + \tau(25) > \tau(4) + \tau(16) + \tau(36).$

What are the last 3 digits of $$N$$?

This problem is posed by Derek K.

Details and assumptions

A permutation $$\tau$$, on a set $$S$$, is a bijection from $$S$$ onto itself. $$\tau(s)$$ denotes the image of the element $$s$$ under this map.

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