Let f : mathbbR to mathbbR$f : \mathbb{R} \to \mathbb{R}$ be a function defined by f(x) = frac4^x4^x + 2$f(x) = \frac{4^x}{4^x + 2}$ and M = int_f(a)^f(1 - a) x sin^4(x(1 - x)) dx$M = \int_{f(a)}^{f(1 - a)} x \sin^4(x(1 - x)) dx$, N = int_f(a)^f(1 - a) sin^4(x(1 - x)) dx; a neq frac12$N = \int_{f(a)}^{f(1 - a)} \sin^4(x(1 - x)) dx; a \neq \frac{1}{2}$. If alpha M = beta N, alpha, beta in mathbbN$\alpha M = \beta N, \alpha, \beta \in \mathbb{N}$, then the least value of alpha^2 + beta^2$\alpha^2 + \beta^2$ is equal to