You are given a 0-indexed integer array nums of size n representing the cost of collecting different chocolates. The cost of collecting the chocolate at the index i is nums[i]. Each chocolate is of a different type, and initially, the chocolate at the index i is of ith type.
In one operation, you can do the following with an incurred cost of x:
ith type to ((i + 1) mod n)th type for all chocolates.Return the minimum cost to collect chocolates of all types, given that you can perform as many operations as you would like.
\n\n\n
Example 1:
\n\n\nInput: nums = [20,1,15], x = 5\nOutput: 13\nExplanation: Initially, the chocolate types are [0,1,2]. We will buy the 1st type of chocolate at a cost of 1.\nNow, we will perform the operation at a cost of 5, and the types of chocolates will become [1,2,0]. We will buy the 2nd type of chocolate at a cost of 1.\nNow, we will again perform the operation at a cost of 5, and the chocolate types will become [2,0,1]. We will buy the 0th type of chocolate at a cost of 1. \nThus, the total cost will become (1 + 5 + 1 + 5 + 1) = 13. We can prove that this is optimal.\n\n\n
Example 2:
\n\n\nInput: nums = [1,2,3], x = 4\nOutput: 6\nExplanation: We will collect all three types of chocolates at their own price without performing any operations. Therefore, the total cost is 1 + 2 + 3 = 6.\n\n\n
\n
Constraints:
\n\n1 <= nums.length <= 10001 <= nums[i] <= 1091 <= x <= 109给你一个长度为 n 、下标从 0 开始的整数数组 nums ，表示收集不同巧克力的成本。每个巧克力都对应一个不同的类型，最初，位于下标 i 的巧克力就对应第 i 个类型。
在一步操作中，你可以用成本 x 执行下述行为：
ith 修改为类型 ((i + 1) mod n)th。假设你可以执行任意次操作，请返回收集所有类型巧克力所需的最小成本。
\n\n\n\n
示例 1：
\n\n\n输入：nums = [20,1,15], x = 5\n输出：13\n解释：最开始，巧克力的类型分别是 [0,1,2] 。我们可以用成本 1 购买第 1 个类型的巧克力。\n接着，我们用成本 5 执行一次操作，巧克力的类型变更为 [1,2,0] 。我们可以用成本 1 购买第 2 个类型的巧克力。\n然后，我们用成本 5 执行一次操作，巧克力的类型变更为 [2,0,1] 。我们可以用成本 1 购买第 0 个类型的巧克力。\n因此，收集所有类型的巧克力需要的总成本是 (1 + 5 + 1 + 5 + 1) = 13 。可以证明这是一种最优方案。\n\n\n
示例 2：
\n\n\n输入：nums = [1,2,3], x = 4\n输出：6\n解释：我们将会按最初的成本收集全部三个类型的巧克力，而不需执行任何操作。因此，收集所有类型的巧克力需要的总成本是 1 + 2 + 3 = 6 。\n\n\n
\n\n
提示：
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