Counting Soldiers Discreetly

According to Chinese folklore, to avoid spies overhearing the size of his army, general Han Xin gave his messenger only the remainder of soldiers in rectangular formations.

He said, "When my soldiers assemble in rows of 9, four remain; in rows of 11, none remain; in rows of 13, only one remain; in rows of 19, three remain."

Han Xin also told his messenger that the number is the second smallest solution. How many soldiers is he commanding?

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