| # 730_J. Bottles |
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| ## Problem Description |
| Nick has n bottles of soda left after his birthday. Each bottle is described by two values: remaining amount of soda ai and bottle volume bi (ai ≤ bi). |
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| Nick has decided to pour all remaining soda into minimal number of bottles, moreover he has to do it as soon as possible. Nick spends x seconds to pour x units of soda from one bottle to another. |
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| Nick asks you to help him to determine k — the minimal number of bottles to store all remaining soda and t — the minimal time to pour soda into k bottles. A bottle can't store more soda than its volume. All remaining soda should be saved. |
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| Input |
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| The first line contains positive integer n (1 ≤ n ≤ 100) — the number of bottles. |
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| The second line contains n positive integers a1, a2, ..., an (1 ≤ ai ≤ 100), where ai is the amount of soda remaining in the i-th bottle. |
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| The third line contains n positive integers b1, b2, ..., bn (1 ≤ bi ≤ 100), where bi is the volume of the i-th bottle. |
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| It is guaranteed that ai ≤ bi for any i. |
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| Output |
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| The only line should contain two integers k and t, where k is the minimal number of bottles that can store all the soda and t is the minimal time to pour the soda into k bottles. |
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| Examples |
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| Input |
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| 4 |
| 3 3 4 3 |
| 4 7 6 5 |
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| Output |
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| 2 6 |
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| Input |
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| 2 |
| 1 1 |
| 100 100 |
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| Output |
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| 1 1 |
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| Input |
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| 5 |
| 10 30 5 6 24 |
| 10 41 7 8 24 |
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| Output |
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| 3 11 |
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| Note |
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| In the first example Nick can pour soda from the first bottle to the second bottle. It will take 3 seconds. After it the second bottle will contain 3 + 3 = 6 units of soda. Then he can pour soda from the fourth bottle to the second bottle and to the third bottle: one unit to the second and two units to the third. It will take 1 + 2 = 3 seconds. So, all the soda will be in two bottles and he will spend 3 + 3 = 6 seconds to do it. |
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| ## Contest Information |
| - **Contest ID**: 730 |
| - **Problem Index**: J |
| - **Points**: 0.0 |
| - **Rating**: 1900 |
| - **Tags**: dp |
| - **Time Limit**: {'seconds': 2, 'nanos': 0} seconds |
| - **Memory Limit**: 512000000 bytes |
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| ## Task |
| Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases. |
