Let σ be a random permutation of {0,1,…,6}. Let L(σ) be the length of the longest initial monotonic consecutive subsequence of σ not containing 0; for example, L(2,3,4,6,5,1,0)=3,L(3,2,4,5,6,1,0)=2,L(0,1,2,3,4,5,6)=0. If the expected value of L(σ) can be written as nm, where m and n are relatively prime positive integers, then find m+n.