Nurse Mira works in an allergy clinic. For each patient Mira tests (n) allergens in a fixed order. The outcome of the tests is written down as a binary string (x) of length (n): for each allergen, 1 means a positive reaction and 0 means no reaction. To analyze how the reactions are distributed, Mira also writes a parity control string for (x). For a binary string (x) of length (n), the parity control string (y) is defined as follows. For every position (i) ((1 \le i \le n)), let (c_i) be the number of characters equal to 1 among the first (i) characters of (x) (including position (i)). The parity control string (y) is the binary string of length (n) such that (y_i = c_i \mod 2) for all (i) ((1 \le i \le n)). In other words, (y_i) is 1 if (c_i) is odd and 0 if (c_i) is even. For example, if (x = 11101), then (y = 10110). Unfortunately, when recording the data, some bits in the test result string and the parity control string may have been written incorrectly. For a given patient, Mira later finds in the system two binary strings (x') and (y') of the same length (n). They were intended to be some true test result string (x) and its parity control string (y), but some bits in (x) and (y) might have been flipped during recording. For instance, in the previous example only the 3rd bit in (y) could have been flipped, resulting in (x' = 11101) and (y' = 10010). In one bit flip , a position in one of the two strings is chosen and the bit at this position is flipped (changing 0 to 1 or 1 to 0). Mira wants to know the minimal number of bit flips that could have happened when recording the data. Formally, you are given two binary strings (x') and (y') of length (n). You want to obtain two strings (x) and (y) of length (n) from (x') and (y') by flipping some bits in (x') and (y'), so that (y) is