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Next Greater Numerically Balanced Number

An integer x is numerically balanced if for every digit d in the number x, there are exactly d occurrences of that digit in x.

An integer x is numerically balanced if for every digit d in the number x, there are exactly d occurrences of that digit in x.

Given an integer n, return the smallest numerically balanced number strictly greater than n.

Example 1

Input: n = 1

Output: 22

Explanation: 22 is numerically balanced since: - The digit 2 occurs 2 times. It is also the smallest numerically balanced number strictly greater than 1.

Example 2

Input: n = 1000

Output: 1333

Explanation: 1333 is numerically balanced since: - The digit 1 occurs 1 time. - The digit 3 occurs 3 times. It is also the smallest numerically balanced number strictly greater than 1000. Note that 1022 cannot be the answer because 0 appeared more than 0 times.

Example 3

Input: n = 3000

Output: 3133

Explanation: 3133 is numerically balanced since: - The digit 1 occurs 1 time. - The digit 3 occurs 3 times. It is also the smallest numerically balanced number strictly greater than 3000.

Constraints

  • 0 <= n <= 10^6

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