<p>You are given a positive integer <code>n</code>.</p>

<p>Continuously replace <code>n</code> with the sum of its <strong>prime factors</strong>.</p>

<ul>
	<li>Note that if a prime factor divides <code>n</code> multiple times, it should be included in the sum as many times as it divides <code>n</code>.</li>
</ul>

<p>Return <em>the smallest value </em><code>n</code><em> will take on.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 15
<strong>Output:</strong> 5
<strong>Explanation:</strong> Initially, n = 15.
15 = 3 * 5, so replace n with 3 + 5 = 8.
8 = 2 * 2 * 2, so replace n with 2 + 2 + 2 = 6.
6 = 2 * 3, so replace n with 2 + 3 = 5.
5 is the smallest value n will take on.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 3
<strong>Output:</strong> 3
<strong>Explanation:</strong> Initially, n = 3.
3 is the smallest value n will take on.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>
</ul>

from math import sqrt

class Solution:
    def primeFactors(self,n):
        x=0
        while n % 2 == 0:
            x+=2
            n = n // 2

        for i in range(3,int(math.sqrt(n))+1,2):
            while n % i== 0:
                x+=i
                n = n // i
        if n > 2:
            x+=n
        return x

    def isPrime(self,n):
        prime_flag = 0
        if(n > 1):
            for i in range(2, int(sqrt(n)) + 1):
                if (n % i == 0):
                    prime_flag = 1
                    break
            if (prime_flag == 0):
                return True
            else:
                return False
        else:
            return True

    def smallestValue(self, n: int) -> int:
        lst=[0]*100001
        mn=n
        
        while True:
            if lst[n]==1:
                return mn
            if self.isPrime(n):
                return min(n,mn)
            lst[n]=1
            n=self.primeFactors(n)
            mn=min(mn,n)

            
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