\[ 1 \div 2\div 3 \div 4 \div 5 \div 6 \div 7 \]

Add one pair of parentheses to the expression above such that resultant number is an integer and is minimized. Submit your answer as this minimum number.

For instance, we could add the parentheses like \( 1 \div(2\div 3 \div 4 \div 5 \div 6 \div 7) = 1260\), the resultant number of which is an integer but is not necessarily minimized.

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