17675번 - Lamps

There are N lamps in a row at a long hallway. The lamps are numbered from 1 to N. Each lamps has a state of either off or on. There is a special mechanism to change the states of the lamps. In an operation, we can do one of the followings:

• Choose integers p and q with 1 ≤ p ≤ q ≤ N, and make the lamps p, p + 1, . . . , q off.
• Choose integers p and q with 1 ≤ p ≤ q ≤ N, and make the lamps p, p + 1, . . . , q on.
• Choose integers p and q with 1 ≤ p ≤ q ≤ N, and toggle the states of the lamps p, p + 1, . . . , q (off to on, or on to off).

Current states of the lamps are represented by a string A of length N. The i-th (1 ≤ i ≤ N) character of A is 0 if the lamp i is off, and 1 if on. We want to make the states of the lamps to be those represented by a string B of length N, with as few operations as possible. The i-th (1 ≤ i ≤ N) character of B is 0 if we want to make the lamp i off, and 1 if on.

Write a program which, given the number of lamps, the current states and the target states, calculates the minimum number of operations needed to achieve the target states

Read the following data from the standard input.

N
A
B

Write one line to the standard output. The output should contain the minimum number of operations needed to achieve the target states.

• 1 ≤ N ≤ 1 000 000.
• A and B are strings of length N.
• Each character in A and B is either 0 or 1.