AT_ttpc2024_2_h TTPC Never Ends

The abbreviation-deciding machine $ \mathrm{M} $ for a programming contest has a string $ S $ of length $ N $ consisting of uppercase English letters and an integer sequence $ A = (A_1, A_2, \dots, A_N) $ of length $ N $ . Additionally, machine $ \mathrm{M} $ has four cursors numbered from $ 1 $ to $ 4 $ for pointing at characters in $ S $ . Initially, for each $ i = 1, 2, 3, 4 $ , cursor $ i $ points to the $ x_i $ -th character of $ S $ . The machine $ \mathrm{M} $ has two buttons: the **Abbreviation Button** and the **Update Button**. Pressing these buttons triggers the following actions: - **Abbreviation Button**: Machine $ \mathrm{M} $ outputs a string of length $ 4 $ formed by concatenating the characters pointed to by cursors $ 1, 2, 3, 4 $ in this order. - **Update Button**: For each $ i = 1, 2, 3, 4 $ , the following happens: - Let $ y $ be the current position of cursor $ i $ . Cursor $ i $ moves from the $ y $ -th character of $ S $ to the $ A_y $ -th character of $ S $ . This year's programming contest abbreviation was determined by pressing the Abbreviation Button, resulting in `TTPC`. Here, "this year" refers to $ 0 $ years from now. Starting from next year, the abbreviation for the programming contest each year will be obtained through the following steps: 1. Press the update button. 2. Press the abbreviation button to determine the abbreviation. How many years from now will the abbreviation return to `TTPC` for the last time? Will the end of `TTPC` come?

The input is given in the following format: > $ N $ $ S $ $ A_1 $ $ A_2 $ $ \dots $ $ A_N $ $ x_1 $ $ x_2 $ $ x_3 $ $ x_4 $

Output a non-negative integer $ k $ satisfying the following conditions. If such a $ k $ does not exist, output `NeverEnds` instead. - The abbreviation becomes `TTPC` $ k $ years from now. - For any integer $ l > k $ , the abbreviation does not become `TTPC` $ l $ years from now.

### Sample Explanation 1 - $ 0 $ years from now, the abbreviation is `TTPC`, and the cursor positions are $ (1,2,4,5) $ . - $ 1 $ year from now, the abbreviation is `TTPC`, and the cursor positions are $ (2,3,4,5) $ . - $ 2 $ years from now, the abbreviation is `TPPC`, and the cursor positions are $ (3,4,4,5) $ . - $ 3 $ years from now, the abbreviation is `PPPC`, and the cursor positions are $ (4,4,4,5) $ . The last time the abbreviation becomes `TTPC` is 1 year from now. ### Sample Explanation 2 The abbreviation becomes `TTPC` at years $ 0, 4, 8, 12, \dots $ and so on. `TTPC` never ends. ### Constraints - $ N, A_i, x_1, x_2, x_3, x_4 $ are integers. - $ 3 \leq N \leq 50 $ - $ S $ is a string of length $ N $ consisting of uppercase English letters. - $ 1 \leq A_i \leq N\ (1 \leq i \leq N) $ - $ 1 \leq x_1, x_2, x_3, x_4 \leq N $ - $ S_{x_1} = {} $ `T` - $ S_{x_2} = {} $ `T` - $ S_{x_3} = {} $ `P` - $ S_{x_4} = {} $ `C`