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217. Balanced Numbers

A positive integer with k (decimal) digits is called balanced if its first ⌈^k/₂⌉ digits sum to the same value as its last ⌈^k/₂⌉ digits, where ⌈x⌉, pronounced ceiling of x, is the smallest integer ≥ x, thus ⌈π⌉ = 4 and ⌈5⌉ = 5.

So, for example, all palindromes are balanced, as is 13722.

Let T(n) be the sum of all balanced numbers less than 10ⁿ.
Thus: T(1) = 45, T(2) = 540 and T(5) = 334795890.

Find T(47) mod 3¹⁵