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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))

**Constraints:**

1 <= N <= 10^{5}

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Faithful Numbers

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