2 of 3 added 4122 characters in body

First, we can exclude all the spaces around the 0s:

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| 2 |   | 1 | . | 1 |   | 3 |   |   |   |
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|   |   | . | 0 | . |   |   |   | 2 | 1 |
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| 2 |   | . | . | 1 | . | . |   |   |   |
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|   |   | 1 |   | . | 0 | . |   | 3 | . |
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|   |   |   |   | . | . | . |   | . | 0 |
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|   |   | 3 |   | 3 |   |   |   | . | . |
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|   |   |   |   | 2 |   |   | 1 |   |   |
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| . | . |   | 4 |   |   | 1 | . | . | 2 |
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| 0 | . |   |   |   |   | . | 0 | . |   |
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| . | . |   | 3 |   | 2 | . | . | 2 |   |
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The 2 in the bottom right only has two open spaces next to it, so we can fill those in. We also have some squares in the top left with only one possibility.

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| 2 | . | 1 | . | 1 |   | 3 |   |   |   |
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| < | > | . | 0 | . |   |   |   | 2 | 1 |
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| 2 | . | . | . | 1 | . | . |   |   |   |
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| . | . | 1 |   | . | 0 | . |   | 3 | . |
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|   |   |   |   | . | . | . |   | . | 0 |
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|   |   | 3 |   | 3 |   |   |   | . | . |
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|   |   |   |   | 2 |   |   | 1 |   |   |
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| . | . |   | 4 |   |   | 1 | . | . | 2 |
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| 0 | . |   |   |   |   | . | 0 | . | ^ |
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| . | . |   | 3 |   | 2 | . | . | 2 | v |
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The 3 above the 2 in the center requires that there is some part of a ship in the space above and to the left of it:

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| 2 | . | 1 | . | 1 | . | 3 |   |   |   |
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| < | > | . | 0 | . | ? |   |   | 2 | 1 |
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| 2 | . | . | . | 1 | . | . |   |   |   |
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| . | . | 1 | . | . | 0 | . |   | 3 | . |
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|   | . | . | ? | . | . | . |   | . | 0 |
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|   |   | 3 |   | 3 |   |   |   | . | . |
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|   |   |   |   | 2 |   |   | 1 |   |   |
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| . | . |   | 4 |   |   | 1 | . | . | 2 |
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| 0 | . |   |   |   |   | . | 0 | . | ^ |
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| . | . |   | 3 |   | 2 | . | . | 2 | v |
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Now the 3 in the top row has only one possibility that works with the 2-1 to its right, and the 3 below those is left with only 3 spaces around it:

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| 2 | . | 1 | . | 1 | . | 3 | . | . |   |
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| < | > | . | 0 | . | < | x | > | 2 | 1 |
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| 2 | . | . | . | 1 | . | . | . | . | o |
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| . | . | 1 | . | . | 0 | . | ^ | 3 | . |
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|   | . | . | ? | . | . | . | ? | . | 0 |
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|   |   | 3 |   | 3 |   |   |   | . | . |
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|   |   |   |   | 2 |   |   | 1 |   |   |
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| . | . |   | 4 |   |   | 1 | . | . | 2 |
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| 0 | . |   |   |   |   | . | 0 | . | ^ |
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| . | . |   | 3 |   | 2 | . | . | 2 | v |
-----------------------------------------

[wip]

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| 2 |   | 1 |   | 1 |   | 3 |   |   |   |
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| < | > |   | 0 |   | < | x | > | 2 | 1 |
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| 2 |   |   |   | 1 |   |   |   |   | o |
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|   |   | 1 |   |   | 0 |   | ^ | 3 |   |
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| o |   |   | ^ |   |   |   | v |   | 0 |
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|   |   | 3 | x | 3 |   |   |   |   |   |
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| o |   |   | v | 2 |   |   | 1 | o |   |
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|   |   |   | 4 |   |   | 1 |   |   | 2 |
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| 0 |   | < | x | x | > |   | 0 |   | ^ |
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|   |   |   | 3 |   | 2 |   |   | 2 | v |
-----------------------------------------