Tieu owns a pizza restaurant and he manages it in his own way. While in a normal restaurant, a customer is served by following the first-come, first-served rule, Tieu simply minimizes the average waiting time of his customers. So he gets to decide who is served first, regardless of how sooner or later a person comes.
Different kinds of pizzas take different amounts of time to cook. Also, once he starts cooking a pizza, he
cannot cook another pizza until the first pizza is completely cooked. Let's say we have three customers
who come at time t=0, t=1, & t=2 respectively, and the time needed to cook their pizzas is 3
, 9
, & 6
respectively. If Tieu applies first-come, first-served rule, then the waiting time of three customers is 3
,
11
, & 16
respectively. The average waiting time in this case is (3 + 11 + 16) / 3 = 10
. This is not an
optimized solution. After serving the first customer at time t=3, Tieu can choose to serve the third
customer. In that case, the waiting time will be 3
, 7
, & 17
respectively. Hence the average waiting time
is (3 + 7 + 17) / 3 = 9
.
Help Tieu achieve the minimum average waiting time. For the sake of simplicity, just find the integer part
of the minimum average waiting time.
- ! The first line contains an integer N, which is the number of customers.
In the next
N
lines, the ith line contains two space separated numbersTi
andLi
.Ti
is the time whenith
customer order a pizza, andLi
is the time required to cook that pizza.
- ! Display the integer part of the minimum average waiting time.
Constraints
1 ≤ N ≤ 105
0 ≤ Ti ≤ 109
1 ≤ Li ≤ 109
- ! The waiting time is calculated as the difference between the time a customer orders pizza (the time at which they enter the shop) and the time she is served.
- ! Cook does not know about the future orders.
3
0 3
1 9
2 6
9
3
0 3
1 9
2 5
8
Let's call the person ordering at time = 0 as A
, time = 1 as B
and time = 2 as C
. By delivering pizza for
A
, C
and B
we get the minimum average wait time to be
(3 + 6 + 16)/3 = 25/3 = 8.33
the integer part is 8 and hence the answer.