Hosting Contests

Interview

Time limit2sMemory limit512 MB

Summary

Given counts of five problem groups, each usable at one of its allowed difficulty slots, find the maximum number of easy-medium-hard contests.

Level: Medium5 of 10
Topics: Greedy, Binary search
Solved: No attempts yet

Problem

Hyeonjong likes holding programming contests. He has written a great many problems, and now he wants to know how many contests he can hold with them.

One contest consists of three problems: one easy problem, one medium problem, and one hard problem. All three must be on hand before a contest can be held.

Hyeonjong sorted the problems he has written into the following five difficulty groups.

$E$ problems can be used only as an easy problem.
$EM$ problems can be used as an easy problem or as a medium problem.
$M$ problems can be used only as a medium problem.
$MH$ problems can be used as a medium problem or as a hard problem.
$H$ problems can be used only as a hard problem.

Each problem can be used in one contest only, and at one difficulty only.

Write a program that finds the maximum number of contests Hyeonjong can hold.

Input

The first line contains $E$ , $EM$ , $M$ , $MH$ , $H$ , separated by spaces. ( $0 \le E, EM, M, MH, H \le 100{,}000$ )

Output

Print on the first line the maximum number of contests Hyeonjong can hold.

Examples3

Example 1
Input
```
2 2 1 2 2
```
Expected output
```
3
```
Example 2
Input
```
100 100 100 0 0
```
Expected output
```
0
```
Example 3
Input
```
1 2 3 4 5
```
Expected output
```
3
```