The Faculty of Computer Engineering intends to decorate the faculty building for the ICPC contest. For this purpose, two strings of lamps have been prepared, each containing $n$ lamps. After the decorations are completed, the contest secretary is invited to visit the contest environment and give their opinion. During the visit, the secretary notices that the two strings are not identical in terms of which lamps are on or off at each position. Being very fond of symmetry, the secretary asks the person in charge of decorations to make both strings identical in terms of the on/off status of the lamps. While performing this task, the person in charge realizes that due to a technical problem, they cannot change the state of a single lamp individually. In each step, they must change the state of exactly two lamps simultaneously. Note that the two lamps do not necessarily have to belong to the same string, but in each step, two lamps must change their state simultaneously. Being heavily occupied with other matters, they have asked you to assist them in this task.

Input

The first line of the input contains the integer $n$, representing the number of lamps in each string. Each of the second and third lines contains a binary string of length $n$, representing the status of the lamps in each of the two strings. $0$ means the lamp is off, and $1$ means the lamp is on.

Output

If it is possible to make the strings identical under the given conditions, print the minimum number of steps required to make the strings identical. Otherwise, print NO.

Constraints

$1 \le n \le 10^6$

Examples

Input 1

5
00011
11011

Output 1

1

Input 2

7
0101010
1101100

Output 2

NO