Fate Calculation

Given two names and a positive integer \(\mathrm{ST}\), compute the "fate" number of the couple by following these steps:

1. Extract the abbreviations: For each name, extract all uppercase letters (which represent the initials). For example, if the names are JiangYunFan and TangYuRou, the abbreviations are JYF and TYR respectively, and concatenating them produces JYFTYR.
2. Replace letters with numbers: Replace every letter with a number string according to the rule:
   For each letter \(X\), replace it with \(\mathrm{ST}+k\) where \(k\) is such that \(X\) is the \((k+1))\text{-th}\) letter of the English alphabet. In particular:
   \(A \to \mathrm{ST}\), \(B \to \mathrm{ST}+1\), \(C \to \mathrm{ST}+2\), \(...\), \(Z \to \mathrm{ST}+25\).
   For example, if \(\mathrm{ST} = 81\), then \(J\) (the 10th letter) is replaced by \(81+9=90\), \(Y\) is replaced by \(81+24=105\), etc. Concatenating these replacements for JYFTYR produces the number string 901058610010598.
3. Iterative digit reduction: Perform the following operation repeatedly on the number string:
   - For the current string, sum every two adjacent digits and write down the ones digit (i.e. the last digit of the sum) to form a new string.
   - This operation reduces the length of the string by one. Continue the process until the string either becomes exactly 100 or its length is less than or equal to 2 (note that a string starting with a leading zero counts as two digits).
   The final number (after converting the resulting string to an integer, ignoring any leading zeros) is the "fate" number.

Example:

• Names: JiangYunFan and TangYuRou
• Abbreviation: JYFTYR
• With \(\mathrm{ST}=81\), the letter-to-number mapping gives: \(J\to90\), \(Y\to105\), \(F\to86\), \(T\to100\), \(Y\to105\), \(R\to98\); concatenated into 901058610010598.
• After several iterations of adjacent digit summing, the final string becomes 01, which is interpreted as the integer 1 (the couple's fate number).

Your task is to implement a program that, given two names and an integer \(\mathrm{ST}\), computes and prints the fate number.

inputFormat

Input Format:

• The first line contains a string representing the first person's name.
• The second line contains a string representing the second person's name.
• The third line contains a positive integer \(\mathrm{ST}\).

Note: Each name is provided in CamelCase such that each word starts with an uppercase letter. It is guaranteed that each name contains at least one uppercase letter.

outputFormat

Output Format:

Print a single integer: the calculated fate number.

sample

JiangYunFan
TangYuRou
81

1