There is a one-dimensional garden of length n. In each position of the n length garden, a fountain has been installed. The fountain at the ith position has a value a[i] (1 <= i <= n) that describes the coverage limit of fountain i. A fountain can cover the range from the positon max((i-a[i]),1) to min ((i + a[i]),n). In the beginning, all the fountains are switched off. Determine the minimum number of fountains you need to activate so that the whole n length garden will b covered by water.