Carmela has forgotten the password of her safe. However she remembers that:

- The number is a ten digit positive integer using each of the digits from 0 to 9 exactly once.
- The sum of the numbers in the 3rd and 4th positions is equal to the product of the numbers in the 6th and 9th positions.
- The product of the numbers in the 5th and 10th positions is odd.
- The digit in the 2nd position is larger than the digit in the 5th position, which is larger than the digit in the 7th position.
- The digit in the 8th position is larger than the digit in the 6th position, which is larger than the digit in the 2nd position.
- The sum of the digits in the 2nd, 6th, and 9th positions is a perfect square.
- The sum of the digits in the 4th and 9th positions is equal to the digit in the 10th position.
- The sum of the digits in the 1st and 5th positions is equal to the sum of the digits in the 7th and 10th positions.
- The digit in the 9th position is even.

From the above clues, can you help Carmela to crack the password to open the safe?

(In reply to

One straightforward solution by tomarken)

From what i have read it looks like cond 3 was redundant.

Correct me if I am wrong,