check-digitorial-permutation

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Algorithms

You are given an integer <code>n</code>.

A number is called digitorial if the sum of the factorials of its digits is equal to the number itself.

Determine whether any permutation of <code>n</code> (including the original order) forms a digitorial number.

Return <code>true</code> if such a permutation exists, otherwise return <code>false</code>.

Note:

<ul>
	<li>The factorial of a non-negative integer <code>x</code>, denoted as <code>x!</code>, is the product of all positive integers less than or equal to <code>x</code>, and <code>0! = 1</code>.</li>
	<li>A permutation is a rearrangement of all the digits of a number that does not start with zero. Any arrangement starting with zero is invalid.</li>
</ul>

&nbsp;
Example 1:

<div class="example-block">
Input: n = 145

Output: true

Explanation:

The number 145 itself is digitorial since <code>1! + 4! + 5! = 1 + 24 + 120 = 145</code>. Thus, the answer is <code>true</code>.
</div>

Example 2:

<div class="example-block">
Input: n = 10

Output: false

Explanation:​​​​​​​

10 is not digitorial since <code>1! + 0! = 2</code> is not equal to 10, and the permutation <code>&quot;01&quot;</code> is invalid because it starts with zero.
</div>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= n &lt;= 109</code></li>
</ul>