# Codeforces Round #332 (Div. 2) D. Spongebob and Squares Math

Source: Internet
Author: User
Tags 3x5 table

D. Spongebob and Squares

Spongebob is already tired trying to reason his weird actions and calculations, so he simply asked you to find all pairs O f N and M, such that there is exactly x distinct squares in the table consisting of n rows and m columns. For example, in a 3x5 table there is 15squares with side one, 8 squares with side and 3 squares W ITH side Three. The total number of distinct squares in a 3x5 table is8 + 3 =.

Input

The first line of the input contains a single integer x (1≤ x ≤10)-the number of Squar Es inside the tables Spongebob is interested in.

Output

First print a single integer k -the number of tables with exactly x distinct squares inside.

Then print k pairs of integers describing the tables. Print the pairs in the order of increasing n, and in case of equality-in the order of increasing m.

Sample Test (s) input
`26`
Output
`61 262 93 55 37 |26 1`
input
`2`
Output
`21 22 1`
input
`8`
Output
`41 82 33 28 1`
Note

In a 1x2 table there is 2 1x1 squares. So, 2 distinct squares in total.

In a 2x3 table there is 6 1x1 squares and 2 2x2 squares. That's equal to 8 squares in total.

Test Instructions : give you x, ask you how many kinds of n*m circumstances make, in the current rectangle within the number of small squares is X

Exercises

Column push: Sigma (K=1,k=min (n,m)) (n-k+1) * (m-k+1) =x;

We enumerate N and get M

`///1085422276#include <bits/stdc++.h>using namespaceStd;typedefLong Longll;#defineMem (a) memset (A,0,sizeof (a))#definePB Push_backinline ll read () {ll x=0, f=1;CharCh=GetChar ();  while(ch<'0'|| Ch>'9'){        if(ch=='-') f=-1; ch=GetChar (); }     while(ch>='0'&&ch<='9') {x=x*Ten+ch-'0'; ch=GetChar (); }returnx*F;}//****************************************Const intn=100000+ -;#defineMAXN 100000+5ll X;intMain () {x=read (); Vector<pair<ll, ll> >ans; ll Sum=0;  for(LL i=1; sum<=x; i++) {sum+=1ll*i*i; Long Longd=x-sum; Long Longk=1ll*i* (i+1)/2; if(d%k==0) {Ans.push_back ({i, D/k+i}); Ans.push_back ({d/k+I, i});    }} sort (Ans.begin (), Ans.end ()); Ans.resize (Unique (Ans.begin (), Ans.end ())-Ans.begin ()); printf ("%d\n", Ans.size ());  for(LL i=0; I<ans.size (); i++) printf ("%i64d%i64d\n", Ans[i].first, Ans[i].second); return 0;}`
Code

Codeforces Round #332 (Div. 2) D. Spongebob and Squares Math

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