# Find number of ways to create sequence \$A\$ of length \$n\$ satisfying \$m\$ conditions

Find number of ways to create sequence $$A$$ of length $$n$$ satisfying $$m$$ conditions. This sequence $$A$$ should consist of only non negative numbers. Each condition is described by three integers $$i,j,k$$ signifying $$max$$($$A_{i}$$,$$A_{j}$$)=$$k$$.
It is guaranteed that each index of the sequence will be there in at least one condition i.e. there will be finite number of such sequences.
The maximum value of $$n$$ will not exceed $$18$$ and maximum value of $$k$$ will not exceed $$2*10^4$$.
I tried it using dynamic programming but the time complexity came out to be exponential. Can you suggest me any better approach which will reduce the time complexity?