First row: average merging history of the main progenitor of Virgo (solid blue line) and random (dashed orange line) candidates. Solid green and dashed violet lines stand for the merging history of the second progenitor of Virgo and random candidates respectively before they merge with the main progenitor. With the same color code, the filled areas denote the standard deviations. Second row: ratio of the constrained to random standard deviations for the main (solid black line) and second (dashed red line) progenitors. Third row: standard deviation of the means (main: solid gray line and second: solid light green line) and standard deviations (main: dashed light blue line and second: dashed pink line) of several sets of 15 random candidates.