12. In the rectangular coordinate system $x O y$, let $P$ be a moving point on the right branch of the hyperbola $x ^ { 2 } - y ^ { 2 } = 1$. If the distance from point $P$ to the line $x - y + 1 = 0$ is always greater than or equal to c, then the maximum value of the real number c is $\_\_\_\_$.\\