 Prime-tuple upper bound from the Selberg sieve

For distinct natural numbers $h_1,\dots ,h_r$,Exclude the fixed primes dividing some $h_i-h_j$ so that the polynomial ${\prod }_i(n+h_i)$ has exactly $r$ roots modulo every remaining prime, then apply the Selberg upper-bound sieve with level $x^{1/4}$.