 Gromov width of the monotone product of projective lines

When each projective line has area $\pi$, the product ${\mathbb{CP}}^1\times {\mathbb{CP}}^1$ has Gromov width $\pi$. The lower bound comes from the product of two area-$\pi$ discs; the upper bound comes from a J-holomorphic sphere of area $\pi$ through the center of any proposed ball.