A company recently discovered that one of its employees, Mary, has been stealing company funds by writing checks to herself and forging the signature of the company's chief financial officer. The company estimates that Mary has stolen a total of $100,000 over the past year. In order to prevent this type of fraud in the future, the company decides to implement a new check verification system that involves using a mathematical formula to calculate a check digit that is added to the end of each check number.

The formula for calculating the check digit is as follows:

1. Start with the first digit of the check number and assign it a weight of 7.
2. Continue assigning weights of 3, 1, 7, 3, 1, 7, 3, 1, in sequence, to the remaining digits of the check number.
3. Multiply each digit by its assigned weight, and add the resulting products together.
4. Divide the sum by 10 and take the remainder.
5. If the remainder is zero, the check digit is zero. Otherwise, subtract the remainder from 10 to get the check digit.

Mary is aware of the new check verification system and decides to continue stealing company funds by altering the check digits of the checks she writes. Mary knows that if she alters the check digit, the system will not detect the fraud. To do this, Mary uses the following formula to calculate the new check digit:

1. Start with the first digit of the check number and assign it a weight of 9.
2. Continue assigning weights of 7, 3, 1, 9, 7, 3, 1, 9, in sequence, to the remaining digits of the check number.
3. Multiply each digit by its assigned weight, and add the resulting products together.
4. Divide the sum by 10 and take the remainder.
5. If the remainder is zero, the check digit is zero. Otherwise, subtract the remainder from 10 to get the check digit.

Mary writes a check for $5,000 with the check number 1249. She then alters the check digit to cover her tracks. Calculate the new check digit that Mary would have added to the check number to make it look legitimate.

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