LogiQuest

273. Gas Station Circuit

MediumGreedy

Station i gives gas[i] and travelling to the next costs cost[i]. Print the 0-based index of the station from which you can complete the circle, or -1. The answer is unique if it exists.

Input format

Line 1: n Line 2: gas values Line 3: costs

Output format

The start index, or -1.

Example 1

Input

5
1 2 3 4 5
3 4 5 1 2

Output

3

Example 2

Input

3
2 3 4
3 4 3

Output

-1

Constraints

1 ≤ n ≤ 10⁵

Read input from standard input and print the answer to standard output. Your code is judged against 3 test cases, most of them hidden.

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