Given a time represented in the format "HH:MM", form the next closest time by reusing the current digits. There is no limit on how many times a digit can be reused.

You may assume the given input string is always valid. For example, "01:34", "12:09" are all valid. "1:34", "12:9" are all invalid.

Example 1:

Input:
 "19:34"

Output:
 "19:39"

Explanation:
 The next closest time choosing from digits 
1
, 
9
, 
3
, 
4
, is 
19:39
, which occurs 5 minutes later.  It is not 
19:33
, because this occurs 23 hours and 59 minutes later.

Example 2:

Input:
 "23:59"

Output:
 "22:22"

Explanation:
 The next closest time choosing from digits 
2
, 
3
, 
5
, 
9
, is 
22:22
. It may be assumed that the returned time is next day's time since it is smaller than the input time numerically.

class Solution {
    public String nextClosestTime(String time) {
        int start = 60 * Integer.parseInt(time.substring(0, 2));
        start += Integer.parseInt(time.substring(3));
        int ans = start;
        int elapsed = 24 * 60;
        Set<Integer> allowed = new HashSet();
        for (char c: time.toCharArray()) if (c != ':') {
            allowed.add(c - '0');
        }

        for (int h1: allowed) for (int h2: allowed) if (h1 * 10 + h2 < 24) {
            for (int m1: allowed) for (int m2: allowed) if (m1 * 10 + m2 < 60) {
                int cur = 60 * (h1 * 10 + h2) + (m1 * 10 + m2);
                int candElapsed = Math.floorMod(cur - start, 24 * 60);
                if (0 < candElapsed && candElapsed < elapsed) {
                    ans = cur;
                    elapsed = candElapsed;
                }
            }
        }

        return String.format("%02d:%02d", ans / 60, ans % 60);
    }
}