A kitchen keeps n identical spice jars in a row. Jar i currently holds a string of lowercase letters, where each letter represents one unit of a specific spice already placed inside that jar (e.g. 'c' for a unit of cinnamon). A prep cook is allowed to move any single spice unit from any jar into any other jar, any number of times (jars are not required to keep their original size). Determine whether the cook can reach a state where all n jars end up holding exactly the same blend, meaning that after sorting each jar's letters alphabetically, every jar's resulting string is identical.

Input format

• Line 1: a single integer n, the number of jars.
• Next n lines: each line contains one non-empty string of lowercase English letters, the initial contents of that jar.

Output format

• Print "true" if the jars can be rebalanced so all n end up with an identical blend, and "false" otherwise.

Constraints

• 1 <= n <= 100
• 1 <= length of each jar's string <= 100
• Every character is a lowercase English letter ('a'-'z').

2
aaab
ba

true

2
aab
c

false