A number is called faithful if you can write it as the sum of distinct powers of 7. e.g., 2457 = 7 + 7^{2} + 7^{4 . }If we order all the faithful numbers, we get the sequence 1 = 7^{0}, 7 = 7^{1}, 8 = 7^{0} + 7^{1}, 49 = 7^{2}, 50 = 7^{0} + 7^{2} . . . and so on. Given some value of N, you have to find the N'th faithful number.

Example 1:

Input:
N = 3Output:8Explanation:8 is the 3rd Faithful number.

Example 2:

Input:
N = 7Output:57Explanation:57 is the 7th Faithful number.

Your Task:
You don't need to read input or print anything. Your task is to complete the function nthFaithfulNum() which takes an Integer N as input and returns the answer.

Expected Time Complexity: O(log(N)) Expected Auxiliary Space: O(log(N))