A keen entomologist, Vasya studied an ant population in the neighboring forest. He discovered a huge anthill and, after spending a lot of time, determined that $$$k$$$ ants lived in it.

Due to the imposed quarantine, Vasya could not continue his field research. However, Vasya knows that there are $$$n$$$ anthills in total in the forest, which means that one may try to apply Zipf's law to estimate their size.

Zipf's law states: if $$$k$$$ insects live in the largest anthill, then in the second largest will be approximately half as many ($$$k / 2$$$), in the third three times less ($$$k / 3$$$), and in the $$$i$$$-th largest will live $$$i$$$ times less than ($$$k / i$$$).

Vasya made a forecast – a series of integers $$$c_1, c_2, ..., c_n$$$, where $$$c_i = k / i$$$, rounded to the nearest integer (according to mathematical rules, that is, numbers like $$$1.5, 2.5, ... $$$ were rounded up).

Unfortunately, the ants living on the home ant farm did not appreciate the researcher's impulse and damaged his notes. The saddest thing is that the original number $$$k$$$ was also damaged. However, some of the $$$c_i$$$ numbers have been preserved. Help Vasya recover the lost data.

Write a program that uses the preserved records $$$c_i$$$ to find the minimum initial number $$$k$$$. If there are several such numbers, print the minimum of them.