Question

In a survey of four-year colleges and universities, it was found that

219 offered a liberal arts degree.
102 offered a computer engineering degree.
457 offered a nursing degree.
26 offered a liberal arts degree and a computer engineering degree.
193 offered a liberal arts degree and a nursing degree.
84 offered a computer engineering degree and a nursing degree.
21 offered a liberal arts degree, a computer engineering degree, and a nursing degree.
31 offered none of these degrees.

How many four-year colleges and universities were surveyed?