A network security administrator must protect networks at several locations from cyber-attacks.

Initially, the nth network has num_servers[i] servers, and money[i] funds allocated for security upgrades. To upgrade a server in the n^{th} network, it costs upgrade[i]. Selling a server adds sell[i] to available funds.

Formally, Given the arrays num_servers, money, upgrade, and sell, each with n integers, determine the maximum number of servers that can be upgraded to ensure optimal network security.

The result should be an array of n integers, where the ith integer represents the maximum number of upgraded servers for the ith network system.

Example 1 :

Input: num_servers = [4, 3], money = [8, 9], sell = [4, 2], upgrade = [4, 5]
Output: [3, 2]
Explanation: