If PARTS × 4 = STRAP, what is the number PARTS?

That's exactly like my math-loving friend, Amol. He talks cryptically.

"What do you mean?" I asked.

"Well, PARTS is a five-digit number where the letters are substituted for digits. So, PARTS can be any number; for instance, it can be 34568 where P = 3, A = 4, R = 5, T = 6, and S = 8. Of course, in this case, it is not 34568; I was just giving an example. So, PARTS is a five-digit number where all the digits are distinct (no two of them are the same) and none of them is zero. When you multiply PARTS by 4, you get a number where the digits are reversed; you get STRAP, which is also a five-digit number. Can you tell what number PARTS stands for?

"Sounds simple enough," I said. "I will solve it within minutes."

"Do try," Amol said.

And I have been trying. Minutes have passed, hours have passed, and days have passed; I am still trying. Will you help me solve it?

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