Life in Wartime

War has broken out in Seokhwan. Seokhwan is a nation shaped like an enormous binary tree, made up of $10^{100}$ cities numbered $1, 2, \ldots, 10^{100}$. It has $10^{100}-1$ roads, and for $1 \le i < 10^{100}$, the $i$-th road connects city $\lfloor \frac{i+1}{2} \rfloor$ to city $i+1$. A picture of this is shown below.

Prime Minister Winston Agiseokhwan has taken on the grave task of saving Seokhwan from its crisis. The hostile nations are bent on disrupting Seokhwan's important military facilities, so to protect the people of Seokhwan it is effective to defend first the cities that armies travel through often. In Seokhwan there are $N$ military units stationed in distinct cities, and the units move between cities to exchange supplies and information.

A city is dangerous if a military unit is stationed there, or if there exist two distinct military units whose path passes through that city. Note that Seokhwan is a tree and a path is defined never to visit the same city twice, so the path between any two military units is always unique.

For Prime Minister Agiseokhwan, compute the number of dangerous cities in Seokhwan.

The first line gives the number of military units $N$. ($2 \le N \le 250{,}000$)

The next $N$ lines give the sequence $A_1, \ldots, A_N$ of the numbers of the cities containing military units. The given cities are all distinct. ($1 \le A_i < 250$)

Print the number of dangerous cities in Seokhwan.