U505210 Green Tree

[Chinese Statement](https://www.luogu.com.cn/problem/P11242). **You must submit your code at the Chinese version of the statement.** > Unconstrained, chivalrous but cultivated.

Looking at the sequence of symbols that Trine cannot understand, he decides to tell you about a competitive programming problem first. Trine has a rooted tree with exactly $k$ leaves, whose depths are respectively $a_1\dots a_k$. He want you to help him calculate the minimum number of nodes of such a tree. Trine guarantees that there is at least one such tree. If you are not familiar with some of the definitions in the problem, we would like to remind you: - A **simple path** on a graph is a path that does not go through the same node or edge more than once. - A **tree** is a connected graph, in which each two nodes have only one simple path in between. In a tree, we must select a node as the root. - A **leaf** is a node in a tree, which has a degree of $1$ and is not the root. - The **depth** of a node in a tree is the number of nodes on the simple graph between it and the root.

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In the first sample test case, one possible tree is as shown in the following figure:  which contains $8$ nodes. Leaves $3, 5, 6, 8$ have depths $2, 3, 4, 5$ respectively. It can be proven there is no such tree with $7$ nodes or fewer.