It is well known, that the year on planet Eisiem has n days. Of course, some days are very good for people, while some others are just horrible. Long observations have shown for each day of the year whether this day is good for most people, or bad.
The new president of the Planet Federation wants all people to be happy. He knows that good emotions have a tendency to accumulate, just like bad ones do. The New Year however is a special event and all emotions accumulated by this moment just disappear. Therefore the president wants to change the calendar on Eisiem and choose the new first day of the year, so that the positive emotions would prevail the whole year.
More precisely, for all i from 1 to n let ai be 1 if i-th day is good for most people and -1 if it is bad. Let sjk be the sum of ai for all days from the j-th day of the year to the k-th, that is:
President wants to find such j to order the j-th day to be the first day of the year, that sjk is positive for all k from 1 to n. Since he wants several variants to choose from, he asks you to find all such j. Since he doesn't want to get too much information at once, first of all he wants to know the number of such j. That is exactly your task.
The first line of each test case contains n - the number of days (1 <= n <= 200 000). Next line contains n integer numbers - ai.