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**Medium** - Contributors:
**vchernoy**

You are given coins of different denominations and a total amount of money. Write a function to compute the number of combinations that make up that amount. You may assume that you have infinite number of each kind of coin.

**Note:**
You can assume that

- 0 <= amount <= 5000
- 1 <= coin <= 5000
- the number of coins is less than 500
- the answer is guaranteed to fit into signed 32-bit integer

**Example 1:**

Input:amount = 5, coins = [1, 2, 5]Output:4Explanation:there are four ways to make up the amount: 5=5 5=2+2+1 5=2+1+1+1 5=1+1+1+1+1

**Example 2:**

Input:amount = 3, coins = [2]Output:0Explanation:the amount of 3 cannot be made up just with coins of 2.

**Example 3:**

Input:amount = 10, coins = [10]Output:1

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