Museum Wing Pledge Override

A city museum is expanding and has twelve unfinished wings, numbered 0 through 11 (a wing's number doubles as its naming-rights prestige value). A rival donor has already locked in a pledge for every wing, and you know exactly how much they committed to each one; their twelve pledges add up to a fixed total budget T.

You have been handed that same total budget T to distribute across the twelve wings: choose a non-negative integer pledge for every wing so that all twelve pledges sum to exactly T (any money you don't want to spend chasing a wing must still be assigned somewhere, so it is always safe to park leftover funds on wing 0, which is worthless anyway). For every wing where your pledge is strictly greater than the rival's pledge, you win that wing's naming rights and add its wing number to your score. Wing 0 never contributes to your score even if you win it.

Determine the maximum total score you can achieve.

Input format

• Line 1: a single integer T, the total budget.
• Line 2: twelve space-separated integers riv[0..11], the rival's pledge to each wing.

Output format

A single integer: the maximum achievable score.

Constraints

• 1 <= T <= 100000
• 0 <= riv[i] <= T for every wing
• riv[0] + riv[1] + ... + riv[11] = T

5
5 0 0 0 0 0 0 0 0 0 0 0

45

10
0 1 2 3 0 0 0 0 0 0 0 4

51