Is it possible to calculate standard deviation if I have sum of squares and number of samples as input?

Question

I have following inputs

Sum of the squares of the numbers. For example if the numbers are $1,4,6$ the sum of squares is $53 = 1^2+4^2+6^2$.

And I have the number of input samples: $3$ in this case. Is it possible to calculate the standard deviation?

Note I don't have the actual numbers $1,4$ and $6$ just the sum of their squares that is $53$.

Answer 1

You might note that e.g. $1^2 + 8^2 = 4^2 + 7^2$. Do $\{1,8\}$ and $\{4,7\}$ have the same standard deviation?