We begin in column 1 (for the word Janet) by setting the Viterbi value in each cell to the product of the π transition probability and the observation likelihood of the word Janet given the tag for that cell. Most of the cells in the column are zero since the word Janet cannot be any of those tags. Next, each cell in the will column gets updated. For each state, we compute the value viterbi[s,t] by taking the maximum over the extensions of all the paths from the previous column that lead to the current cell according to $vt(j) =\max_{N \leq i \leq n}v_{t−1}(i) a_{ij}b_{j}(o_{t})$ The remaining value is multiplied by the relevant observation probability, and the (trivial) max is taken.