Given several real numbers x_{1}, …, x_{n}, we want to find the smallest possible set of closed intervals of length 1 that cover those real numbers. In other words, we must find a set of intervals {[y_{1}, y_{1} + 1], …, [y_{m}, y_{m} + 1]} such that
For instance, if the x_{i}’s are 1.4, 1.9, 2.3 i 2.7, a possible solution is {[1.2, 2.2], [1.8, 2.8]}, because every x_{i} is inside of (at least) one of the two intervals, and it is not possible to cover the four real numbers with only one interval.
Input
Input consists of several cases, each with a number n followed by n different real numbers. Assume n ≤ 10^{5}.
Output
For every case, print the minimum number of closed intervals of length 1 that cover the given real numbers.
Input
4 1.4 1.9 2.3 2.7 6 1.75 3.5 0.5 3 1.5 0.2 2 -2.5 -3.5
Output
2 3 1