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Figure 1 the time line for merged spells and initial spells. Each initial spell is transformed into a pair of signed flags. The first initial spell line extends horizontally over the first two time periods, the second initial spell extends from the second to fourth time periods and the third initial spell extends over the fifth and sixth time periods, each has a 1 and minus 1 at the beginning and end of the line extension. The merged spells are constructed from those time points where the cumulative summations of flags are 1s and 0s along the linear calendar time axis. Thus, the first merged spells line extends over the same time periods as the first and second initial spells and second merged spells line extends over the same periods as the third initial spells line.