# Project Euler Problem 917 – Number Splitting

We define an S-number to be a natural number, $$n$$, that is a perfect square and its square root can be obtained by splitting the decimal representation of n into 2 or more numbers then adding the numbers.

For example, 81 is an S-number because $$\sqrt{81} = 8 + 1$$.
6724 is an S-number: $$\sqrt{6724} = 6 + 72 + 4$$.
8281 is an S-number: $$\sqrt{8281} =8 + 2 + 81 = 82 + 8 + 1$$.
9801 is an S-number: $$\sqrt{9801} = 98 + 0 + 1$$.

Further we define $$T(N)$$ to be the sum of all S numbers $$n ≤ N$$.  You are given $$T(10^4) = 41333$$.

Find $$T(10^{12})$$.

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