Ascending Letters

26 letters of the alphabet are shuffled and listed to form a 26 lettered string. The longest sequence of alphabetically ascending letters (either from left to right or from right to left) in this string is noted. What is the minimum possible number of letters in this sequence?

Two examples for the first seven (A, B, C, D, E, F, G) letters:
Arrangement: BGEDFCA, Longest sequence: GEDCA (ascending from right to left).
Arrangement: DBCAGEF, Longest sequence: BCEF (ascending from left to right)

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