A number is formed in the following manner: 123...(n-2)(n-1)n(n-1)(n-2)...321.
For example: 12345678987654321
Prove that:
The sum of the digits of the number always results in a perfect square of n.
Example 1: 12321: 1+2+3+2+1 = 9 = 3²
Example 2: 12345654321: 1+2+3+4+5+6+5+4+3+2+1 = 36 = 6²