A remote seed vault stamps every incoming batch with a fixed-length alphanumeric code and appends it to the ledger strictly in arrival order. The ledger's retrieval scanner checks the codes one character position at a time: for a single position (the same position across every code), it reads down the ledger from the first entry to the last and requires that character to never decrease. A stamping defect can make one or more positions violate this — at that position, some later entry's character comes before some earlier entry's character in ordinary character order. Before trusting the scanner, the vault keeper must strike every defective position out of the ledger entirely, removing that same position from every single code, at a cost of one unit of restamping effort per position struck out. A position may be kept only if, read from the first entry down to the last, its characters never decrease; whether a position may be kept does not depend on any other position.

Determine the minimum number of character positions the keeper must strike out so that every remaining position is non-decreasing from the first ledger entry to the last.

Input format

Line 1: two integers n and L — the number of ledger entries and the fixed code length. Next n lines: one code each, a string of exactly L characters, each a lowercase English letter or a digit.

Output format

Print a single integer: the minimum number of character positions that must be struck out.

Constraints

• 1 <= n <= 1000
• 1 <= L <= 1000
• Every code consists only of lowercase English letters ('a'-'z') and digits ('0'-'9'), and has length exactly L.

3 2
ca
bb
ac

1

3 3
zyx
wvu
tsr

3