Packing Balls 2

The balls come in $K$ colors. A color is an integer from 1 to $K$, and there are $X_i$ balls of color $i$.

You want to pack all of the balls into boxes. One box holds at most $K$ balls.

The balls inside one box must all have different colors, or must all have the same color.

Write a program that finds the minimum number of boxes you need.

The first line contains the number of colors $K$. ($1 \le K \le 100{,}000$)

The second line contains $X_1, X_2, \dots, X_K$, the ball counts of color 1 through color $K$, separated by spaces. ($1 \le X_i \le 1{,}000{,}000{,}000$)

Print the minimum number of boxes on the first line.