What is the minimum number of small squares that must be colored black so that a line of symmetry lies on the diagonal BD of square ABCD?
[asy]defaultpen(linewidth(1));
for ( int x = 0; x < 5; ++x )
{
draw((0,x)--(4,x));
draw((x,0)--(x,4));
}fill((1,0)--(2,0)--(2,1)--(1,1)--cycle);
fill((0,3)--(1,3)--(1,4)--(0,4)--cycle);
fill((2,3)--(4,3)--(4,4)--(2,4)--cycle);
fill((3,1)--(4,1)--(4,2)--(3,2)--cycle);
label("A", (0, 4), NW);
label("B", (4, 4), NE);
label("C", (4, 0), SE);
label("D", (0, 0), SW);[/asy]<spanclass=′latex−bold′>(A)</span>1<spanclass=′latex−bold′>(B)</span>2<spanclass=′latex−bold′>(C)</span>3<spanclass=′latex−bold′>(D)</span>4<spanclass=′latex−bold′>(E)</span>5