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When a small triangle is surrounded by 3 other small triangles, the result is called a four-triangle. (Of the four-triangles in the diagram, one is shaded). If the integers 1 through 9 are written in the 9 small triangles at the right, 1 per triangle, so that the sum of the 4 integers in each four triangle is the same, what is the least possible value of this sum?
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