I. A Small Game - 2021 年东华大学金马程序设计联赛

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This is a simple question. This is a simple question.This is a simple question.

You are given four integers $N, A, B$ and $C$ .

Now you have a integer $K$ ( $K = 0$ initially).

Each time you can choose one of the following operations:

Cost $A$ and gain $K + 1$ ( $K \to K + 1$ )
Cost $B$ and gain $K \times 2$ ( $K \to K \times 2$ )
Cost $C$ and gain $K - 1$ ( $K \to K - 1$ )

Find the minimun cost to get $N$ .

输入格式

There are multiple test cases in this problem. $(T \leq 10^{5} + 5)$

In each test case,there is only one line contains four integers $N (1 \leq N \leq 10^{9})$ , $A (0 \leq A \leq 10^{9})$ , $B (0 \leq B \leq 10^{9})$ , $C (0 \leq C \leq 10^{9})$ .

输出格式

For each test case print one line for the minimun cost to get $N$ .

样例

Input

Output

NaN

A. Smart AEMShana！ B. Genshin Impact C. Back D. Move the numbers E. A Similar Game F. It is Quite Big G. IDEA's Tree H. A Simple Game I. A Small Game J. A Special Game K. AEMShana loves games！

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2021 年东华大学金马程序设计联赛

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