HJS

Interview

Time limit1sMemory limit1024 MB

Summary

Given three H/J/S patterns of equal length, check whether distinct digits 1 to 9 can be assigned to H, J, and S so that the numbers satisfy p < q < r.

Level: Medium4 of 10
Topics: Brute force, Implementation, String
Solved: No attempts yet

Problem

In 2123, a different way to express numbers exists, called the Hongjin number.

A Hongjin number is a string made of three characters, H, J, and S. Assign the digits 1 through 9 to H, J, and S, each to a different digit, and the string represents a number. For example, the Hongjin number HJSHJH can represent 358353 and 914919, but it cannot represent 131131 or 555555.

Given three Hongjin numbers P, Q, and R of the same length, check whether there exist assignments of H, J, and S such that the numbers p, q, and r represented by P, Q, and R satisfy $p < q < r$ . The digits assigned to H, J, and S are shared by P, Q, and R.

Input

The first line contains N, the length of P, Q, and R. The next three lines contain the strings P, Q, and R in that order. $(1 \le N \le 300\,000)$

Output

If there exist assignments of H, J, and S that satisfy the condition, print HJS! HJS! HJS! on the first line. Otherwise, print Hmm... on the first line.

Examples2

Example 1
Input
```
6
HJSHJS
JHSJHS
SHJSHJ
```
Expected output
```
HJS! HJS! HJS!
```

Example 2

Input

10
HHJHSSHJJH
HHJHHJHJJS
HHJSHJHJSJ

Expected output

Hmm...