Let the image of parabola x^2=4 y, in the line x-y=1 be (y+a)^2=b(x-c), a, b, c ∈ N. Then a+b+c is equal to

Let the image of parabola $\displaystyle x^2=4 y$, in the line $\displaystyle x-y=1$ be $\displaystyle (y+a)^2=b(x-c)$, $\displaystyle a, b, c \in \mathrm{~N}$. Then $\displaystyle a+b+c$ is equal to