思考题 about cheating

Lottery Cheating

Let's have some lottery!

In this lottery system, a number string S and an array of integers A is predetermined. It is known that |A|=|S| and let's define .

Each user chooses a number string T(|T|=|S|). The amount of money he will get equals to . That is to say, it depends on the number of identical digits of S and T.

For example, if A=[1,10,100] and S="019"

if T="000" you will get 1 yuan
if T="011" or "119" you will get 10 yuan
if T="019" you will get 100 yuan
if T="888" you will get 0 yuan sadly

But as a bussinessman, you want to do some cheats. You are given the users' chosen numbers Ts and the sequence A, find such a string S that you need to pay the least money. Print the string.

Example

Input 1
A={1,10,100}
Ts={"110","512","777"}
Output 1
999
Explain 1
The total money you need to pay is 0. Hooray!
Input 1
A={1,10,100,1000,10000}
Ts={"12345","23456","34567","45678","56789","67890","78901","89012","90123","01234"}
Output 1
11111
Explain 1
The total money you need to pay is 1+0+0+0+0+0+1+1+1+1=5

Constriants

Subtask 1(20%):For each ,
Subtask 2(20%): For each ,
Subtask 3(20%):
Subtask 4(40%):.For each ,

No cheating!