# **F. Git Gud** **Time limit:** 2 seconds **Memory limit:** 256 megabytes You are an adventurer working for the futuristic corporation **RoboCorp**. Your current skill level is an integer **s** in the range: [ 1 \le s \le n ] —but you **don’t know its exact value**. Your goal is to reach **skill ≥ n** by completing missions. Each mission costs robocoins. You can choose missions of **any difficulty y** (positive integer) and **any positive duration l** (hours). The cost of a mission depends on: * the new mission’s **duration l** * the relation between the new mission’s **difficulty y** and your **most recent mission’s difficulty x** Let **x** be the difficulty of your most recent mission. If you want to undertake a new mission with **difficulty y** and **duration l**: * If it is your **first mission**, or if **y ≤ x**, **cost = l** * If **y > x**, **cost = l + 1000** Your skill improves only when you do a mission whose difficulty **exactly equals** your **current unknown skill**. * If **y = s**, then your new skill becomes **s += l** * Otherwise, the skill does not change After each mission, you *still don’t know your skill*. You start with a budget of **10⁶ robocoins**. Your task is to produce **any sequence of missions** that **never exceeds this budget**, and **guarantees** that your final skill is **at least n**, regardless of the initial skill. --- # **Input** A single integer **n** (either `4` or `250000`): the required final skill level. There are **2 tests** in this problem (including the example). * Example input is **n = 4** * The real system test uses **n = 250000** Hacks are disabled. --- # **Output** * First line: integer **k** — number of missions you will take. * Next **k** lines: two integers per line **y, l** — the mission’s difficulty and duration with [ 1 \le y, l \le 10^6 ] These missions must guarantee that your final skill ≥ n for *any* starting skill in `[1, n]`. --- # **Example** **Input** ``` 4 ``` **Output** ``` 4 1 4 3 1 2 1 3 1 ``` --- # **Explanation (from PDF)** For the target skill **n = 4**, a valid strategy: 1. Mission difficulty **1**, duration **4** Cost = 4 2. Mission difficulty **3**, duration **1** Previous was 1, so 3 > 1 → Cost = 1 + 1000 = 1001 3. Mission difficulty **2**, duration **1** Previous was 3, so 2 ≤ 3 → Cost = 1 4. Mission difficulty **3**, duration **1** Previous was 2 → 3 > 2 → Cost = 1 + 1000 = 1001 Total cost = 2007 ≤ 10⁶ (budget ok) This strategy guarantees skill ≥ 4 for any initial skill 1–4.