Problem Brief

Maximize Similarity

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In the world of Amazon's vast inventory management, you face a challenge of optimizing two inventories, inv1 and inv2, each containing n elements.

Your goal is to maximize the similarity between these inventories. The similarity is measured by the number of indices i (0 ≤ i < n) where inv1[i] equals inv2[i].

Amazon provides a unique tool, the "Inventory Optimizer". This tool allows you to perform the following operation:

Select two distinct indices i and j (where 0 ≤ i, j < n and i ≠ j), provided that the jth element of inv1 is positive.

Apply the operation: add 1 to inv1[i] and subtract 1 from inv1[j].

Using the Inventory Optimizer, you can perform this operation any number of times (including zero) to maximize the similarity between inv1 and inv2.

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1Example 1

Input

inv1 = [2, 4, 1], inv2 = [1, 2, 3]

Output

Explanation

Apply the operation on indices i = 2 and j = 0, which makes inv1 = [1, 4, 2].
Next, apply the operation on indices i = 2 and j = 1, which updates inv1 = [1, 3, 3].

Now, there are two indices, i = 0 and i = 2, for which inv1[i] = inv2[i]. Since it's impossible to make the elements at all indices of the two arrays equal, the answer is 2.

Constraints

Limits and guarantees your solution can rely on.

1 <= n <= 10^5

1 <= inv1[i], inv2[i] <= 10^4