because of the lexicographic order of the suffix array, every common prefix of the suffixes formula_126 and formula_119 has to be a common prefix of all suffixes between formula_8's position in the suffix array formula_129 and formula_9's position in the suffix array formula_131. therefore, the length of the longest prefix that is shared by "all" of these suffixes is the minimum value in the interval formula_132. this value can be found in constant time if formula_18 is preprocessed for range minimum queries.