Little Monk has N number of toys, where each toy has some width Wi. Little Monk wants to arrange them in a pyramdical way with two simple conditions in his mind. The first being that the total width of the ith row should be less than (i+1)th row. The second being that the total number of toys in the ith row should be less than (i+1)th row. Help Monk find the maximum height which is possible to be attained!
Note: It is NOT necessary to use all the boxes.
The first line contains an integer N, which denotes the number of Monk's toys. The next line contains N integers each denoting the width of the Monk's every single toy.
Print the maximum height of the toy pyramid.
$$1$$ ≤ N ≤ $$10^6$$
$$1$$ ≤ Ni ≤ $$10^9$$
On the lowest level, we can place $$20$$ and $$100$$, and on top of it we can place $$40$$, so the maximum height would be $$2$$.