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An ugly number is a positive integer that is divisible by a, b, or c.

Given four integers n, a, b, and c, return the nth ugly number.

 

Example 1:

Input: n = 3, a = 2, b = 3, c = 5
Output: 4
Explanation: The ugly numbers are 2, 3, 4, 5, 6, 8, 9, 10... The 3rd is 4.

Example 2:

Input: n = 4, a = 2, b = 3, c = 4
Output: 6
Explanation: The ugly numbers are 2, 3, 4, 6, 8, 9, 10, 12... The 4th is 6.

Example 3:

Input: n = 5, a = 2, b = 11, c = 13
Output: 10
Explanation: The ugly numbers are 2, 4, 6, 8, 10, 11, 12, 13... The 5th is 10.

Example 4:

Input: n = 1000000000, a = 2, b = 217983653, c = 336916467
Output: 1999999984

 

Constraints:

  • 1 <= n, a, b, c <= 109
  • 1 <= a * b * c <= 1018
  • It is guaranteed that the result will be in range [1, 2 * 109].

class Solution { public int nthUglyNumber(int n, int a, int b, int c) { } }