B. Baja Shrimp
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

The Baja Shrimp Taco is one of Torchys' most popular tacos. As the shrimp taco is so popular, customers have already scheduled their orders for the next $$$n$$$ days!

Initially, the store has 0 pounds of shrimp. Every morning, the store is scheduled to receive a shipment of $$$s_i$$$ pounds of shrimp. Any leftover shrimp will carry over into the next day. Alice, the store manager, is worried that the store will not have enough shrimp to fulfill the customers' orders on any given day. Being the diligent manager she is, Alice may contact the shrimp supplier and ask that the delivery dates of a single pair of shipments be swapped. She may do this operation exactly once, or not at all.

Can Alice ensure that the store always has enough shrimp to fulfill the customers' orders on any given day?

Input

The first line will contain the integer $$$n$$$ $$$(1 \leq n \leq 2 \cdot 10^5)$$$, the number of days.

The second line will contain the array $$$s$$$ of length $$$n$$$. On the $$$i$$$th day, the store will receive $$$s_i$$$ $$$(0 \leq s_i \leq 10^9)$$$ pounds of shrimp before opening for business.

The third line will contain the array $$$c$$$ of length $$$n$$$. On the $$$i$$$th day, customers will demand $$$c_i$$$ $$$(0 \leq c_i \leq 10^9)$$$ pounds of shrimp.

Output

Output a single line: "Yes" if every customer's order can be fulfilled, or "No" if they cannot.

Examples
Input
5
4 3 1 6 10
4 4 3 5 6
Output
Yes
Input
5
1 2 3 4 5
5 4 3 2 1
Output
No
Input
5
3 2 3 1 7
4 3 3 3 3
Output
Yes
Note

In the first testcase, Alice should swap the first and fifth shipment. In the second testcase, it can be shown that there will be a day in which the customers' orders cannot be fulfilled. In the third testcase, Alice must swap the first and fifth shipment.