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

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

6
1 26
2 9
3 5
5 3
7 |
26 1

input

2

Output

2
1 2
2 1

input

8

Output

4
1 8
2 3
3 2
8 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