In ancient China, generals counted soldiers remaining after a battle by lining them up in rows of diļ¬erent lengths.

If a general had \(1200\) soldiers at the start of a battle and if there were

\(1)\) \(3\) left over when they lined up \(5\) at a time;

\(2)\) \(3\) left over when they lined up \(6\) at a time;

\(3)\) \(1\) left over when they lined up \(7\) at a time;

\(4)\) none left over when they lined \(11\) at a time,

how many soldiers survived the battle?

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