As Many Times as Its Value

Easy

You are given an integer array numbers. Call a number **honest** if it appears in the array exactly as many times as its own value: 2 twice, 5 five times, and so on. Return the largest honest number. If there is none, return -1.

Example 1

numbers=[3, 1, 3, 4, 3] → 3

3 occurs 3 times and 1 occurs once. Both qualify, and the larger is 3.

Example 2

numbers=[2, 5, 5] → -1

2 occurs once and 5 occurs twice, so no number qualifies.

Example 3

numbers=[1] → 1

Constraints

1 ≤ len(numbers) ≤ 10⁵
1 ≤ numbers[i] ≤ 500

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Topics

Array Hash Table Counting

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Input

numbers=[3, 1, 3, 4, 3]

Expected

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