Product of Totatives-II Googol

Let $\mathbb P$ be the product of all possible positive integers $a\leq10^{100}$ such that $\gcd(a,10^{100})=1$ .

Enter sum of digits of $R$ , where $R$ is the remainder when $\mathbb P$ is divided by $10^{100}$ .

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Notation: $\gcd(\cdot)$ denotes the greatest common divisor function.

Hint : If you're stuck, solving this first might give you some insights regarding how to proceed.