Gas Station Circular Tour

EXTREME · C · 5000ms

Finally, coordinating a relay road-trip with limited fuel at each rest stop, Mitu needs to find a valid starting stop from which the whole circular route can be completed without running out of gas. Given N gas stations arranged in a circle, each with gas[i] available and cost[i] to travel to the next station, determine the starting station index (0-indexed) from which you can complete the full circular tour, or print -1 if impossible. Solve in O(N), not O(N^2).

Input

Line1: N. Line2: N gas values. Line3: N cost values.

Output

Starting index (0-indexed), or -1.

Constraints

1 ≤ N ≤ 10^5

Sample Input

5
1 2 3 4 5
3 4 5 1 2

Sample Output

3
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Gas Station Circular Tour · DIU ContestHub