Each year, Aziz Mansour, a local shopkeeper, lights up lanterns (fawanis) in the streets around his shop to celebrate Ramadan. The lanterns are represented by a string of bits, where $$$1$$$ symbolizes a lit lantern and $$$0$$$ symbolizes an unlit lantern.
To maintain tradition, the fawanis must follow a harmonious pattern: the number of $$$01$$$-substrings (a lit lantern followed by an unlit one) must be equal to the number of $$$10$$$-substrings (an unlit lantern followed by a lit one).
However, this year, Mansour has committed an error and the pattern may have become unbalanced. Your task is to help Mansour restore harmony to the lanterns by making the fewest changes.
In one change, you may flip any bit in the string (change a $$$1$$$ to $$$0$$$ or vice versa) to achieve the balanced pattern.
The first line contains a number $$$N$$$: the length of the string. $$$2\le N \le 10^6$$$
The second line contains a string $$$S$$$, the string modeling the lanterns
Output two lines:
2 10
1 0
3 101
0