which is only non-zero for N off-diagonal elements. However, the final expression of R requires a sum of n0,ñ0 . To further reduce the cost, we use the focusing algorithm and the stochastic important sampling to obtain the initial mapping variables, which, upon trajectory average, results in the same answer as if explicitly performing the sum n0,ñ0 . For each trajectory, we use the focused initial condition for the mapping variables, with