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 √81 = 8 + 1.
- 6724 is an S-number: √6724 = 6 + 72 + 4.
- 8281 is an S-number: √8281 = 8 + 2 + 81 = 82 + 8 + 1.
- 9801 is an S-number: √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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