J, 44 bytes
(m]\u:49+i.9),.(m=.,}.@|.)]\&.(|."1)u:97+i.9
I tried to generate numerically a mask of 1 and zero to use for indexing, but the cost of getting rid of the extra row was high and I gave up:
(9-.~i.18){0<:-/~(,|.)i.9
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1
1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1
1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1
1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1
1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1
1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1
1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1
1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1
1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1
1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1
1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1