A farmer has a rectangular field with dimensions 120 meters by 80 meters. He plants crops in half of the field, and in the other half, he builds a barn in the shape of a square with side length equal to half the width of the field. He fences the remaining area of the barn side for grazing. The cost to plant crops is $5 per square meter, and the cost to build the barn is $200 per square meter. If the farmer sells the crops for $10 per square meter, what is his profit or loss? Let's think step by step and output the final answer within \boxed{}.
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