Little Vasya went to the supermarket to get some groceries. He walked about the supermarket for a long time and got a basket full of products. Now he needs to choose the cashier to pay for the products.
There are n cashiers at the exit from the supermarket. At the moment the queue for the i-th cashier already has ki people. The j-th person standing in the queue to the i-th cashier has mi,j items in the basket. Vasya knows that:
Of course, Vasya wants to select a queue so that he can leave the supermarket as soon as possible. Help him write a program that displays the minimum number of seconds after which Vasya can get to one of the cashiers.
The first line contains integer n (1≤n≤100)− the number of cashes in the shop. The second line contains n space-separated integers: k1,k2,...,kn (1≤ki≤100), where ki is the number of people in the queue to the i-th cashier.
The i-th of the next n lines contains ki space-separated integers: mi,1,mi,2,...,mi,ki (1≤mi,j≤100)− the number of products the j-th person in the queue for the i-th cash has.
Print a single integer − the minimum number of seconds Vasya needs to get to the cashier.
1
1
1
20
4
1 4 3 2
100
1 2 2 3
1 9 1
7 8
100
In the second test sample, if Vasya goes to the first queue, he gets to the cashier in 100·5+15=515 seconds. But if he chooses the second queue, he will need 1·5+2·5+2·5+3·5+4·15=100 seconds. He will need 1·5+9·5+1·5+3·15=100 seconds for the third one and 7·5+8·5+2·15=105 seconds for the fourth one. Thus, Vasya gets to the cashier quicker if he chooses the second or the third queue.