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Digital Square

Time Limit:1000MS     Memory Limit:32768KB     64bit IO Format:%I64d & %I64u

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Description

Given an integer N,you should come up with the minimum nonnegative integer M.M meets the follow condition: M²%10^x=N (x=0,1,2,3....)

 

Input

The first line has an integer T( T< = 1000), the number of test cases. 
For each case, each line contains one integer N(0<= N <=10⁹), indicating the given number.

 

Output

For each case output the answer if it exists, otherwise print “None”.

 

Sample Input

3

3

21

25

 

Sample Output

None

11

5

 

 

 #include <iostream>
 #include <stdio.h>
 #include <set>
 #include <string.h>
 #include <algorithm>
 #include <queue>
 using namespace std;
 #define ll long long
 ll n,nu,ans;
 void init()
 {
     ll nn=n;
     nu=;
     while(nn)
     {
         nn/=;
         nu*=;
     }
 }
 bool fun()
 {
     int i,ok=;
     ans=n;
     ll now,x,y,noww;
     queue<pair<ll,ll> >q;
     while(!q.empty())
     q.pop();
     q.push(make_pair(,));
     while(!q.empty())
     {
         x=q.front().first;
         now=q.front().second;
         noww=now*;
         q.pop();
         for(i=;i<;i++)
         {
             y=x+now*i;
             if(y*y%nu==n){ans=min(ans,y);ok=;}
             else
             if(y*y%noww==n%noww)q.push(make_pair(y,noww));
         }
     }
     if(ok)return ;
     return ;
 }
 int main()
 {
     int t;
     scanf("%d",&t);
     while(t--)
     {
         cin>>n;
         if(n==)
         {
             cout<<<<endl;
             continue;
         }
         init();
         if(fun())
         {
             cout<<ans<<endl;
         }
         else printf("None\n");
     }
 }