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| #include<bits/stdc++.h>
using namespace std;
#define enter fout<<"\n";
#define space fout<<" ";
#define dot fout<<",";
#define oui fout<<"Yes\n";
#define non fout<<"No\n";
#define si fout<<"?";
#define i32 int
#define u32 unsigned int
#define i64 long long
#define u64 unsigned long long
#define i128 __int128
#define u128 unsigned __int128
#define debug(x) fout<<#x<<"="<<x<<"\n";
#define vdebug(a,n) fout<<#a<<"=[";for(int i=0;i<=n;++i)fout<<a[i]<<" ";fout<<"]\n";
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
namespace fastio{
const int bufl=1<<20;
const double base1[16]={1,1e-1,1e-2,1e-3,1e-4,1e-5,1e-6,1e-7,1e-8,1e-9,1e-10,1e-11,1e-12,1e-13,1e-14,1e-15};
const double base2[16]={1,1e1,1e2,1e3,1e4,1e5,1e6,1e7,1e8,1e9,1e10,1e11,1e12,1e13,1e14,1e15};
struct IN{
FILE *IT;char ibuf[bufl],*is=ibuf,*it=ibuf;
IN(){IT=stdin;}IN(char *a){IT=fopen(a,"r");}
inline char getChar(){if(is==it){it=(is=ibuf)+fread(ibuf,1,bufl,IT);if(is==it)return EOF;}return *is++;}
template<typename Temp>inline void getInt(Temp &a){a=0;int b=0,c=getChar();while(c<48||c>57)b^=(c==45),c=getChar();while(c>=48&&c<=57)a=(a<<1)+(a<<3)+c-48,c=getChar();if(b)a=-a;}
template<typename Temp>inline void getDouble(Temp &a){a=0;int b=0,c=getChar(),d=0;__int128 e=0,f=0;while(c<48||c>57)b^=(c==45),c=getChar();while(c>=48&&c<=57)e=(e<<1)+(e<<3)+c-48,c=getChar();if(c==46){c=getChar();while(c>=48&&c<=57)d++,f=(f<<1)+(f<<3)+c-48,c=getChar();}a=e+base1[d]*f;if(b)a=-a;}
IN& operator>>(char &a){a=getChar();while(a<=32)a=getChar();return *this;}
IN& operator>>(char *a){do{*a=getChar();}while(*a<=32);while(*a>32)*++a=getChar();*a=0;return *this;}
IN& operator>>(string &a){a.clear();char b=getChar();while(b<=32)b=getChar();while(b>32)a+=b,b=getChar();return *this;}
IN& operator>>(int &a){getInt(a);return *this;}
IN& operator>>(long long &a){getInt(a);return *this;}
IN& operator>>(__int128 &a){getInt(a);return *this;}
IN& operator>>(float &a){getDouble(a);return *this;}
IN& operator>>(double &a){getDouble(a);return *this;}
IN& operator>>(long double &a){getDouble(a);return *this;}
};
struct OUT{
FILE *IT;char obuf[bufl],*os=obuf,*ot=obuf+bufl;int Eps;long double Acc;
OUT(){IT=stdout,Eps=6,Acc=0.5;}OUT(char *a){IT=fopen(a,"w"),Eps=6,Acc=0.5;}
inline void ChangEps(int x=6){Eps=x;}
inline void flush(){fwrite(obuf,1,os-obuf,IT);os=obuf;}
inline void putChar(int a){*os++=a;if(os==ot)flush();}
template<typename Temp>inline void putInt(Temp a){if(a<0){putChar(45);a=-a;}if(a<10){putChar(a+48);return;}putInt(a/10);putChar(a%10+48);}
template<typename Temp>inline void putLeading(Temp a,int b){if(!b)return;putLeading(a/10,b-1);putChar(a%10+48);}
template<typename Temp>inline void putDouble(Temp a){if(a<0){putChar(45);a=-a;}__int128 ff=(a-(__int128)a)*base2[Eps+2],gg=0;ff+=50;while(ff>0){ff/=10;gg++;}__int128 b=a;if(gg==Eps+3){putInt(b+1);}else{putInt(b);}a-=b;a*=base2[Eps];b=a+Acc;putChar(46);putLeading(b,Eps);}
OUT& operator<<(char a){putChar(a);return *this;}
OUT& operator<<(const char *a){while(*a)putChar(*a++);return *this;}
OUT& operator<<(string a){for(auto c:a)putChar(c);return *this;}
OUT& operator<<(int a){putInt(a);return *this;}
OUT& operator<<(long long a){putInt(a);return *this;}
OUT& operator<<(__int128 a){putInt(a);return *this;}
OUT& operator<<(unsigned int a){putInt(a);return *this;}
OUT& operator<<(unsigned long long a){putInt(a);return *this;}
OUT& operator<<(unsigned __int128 a){putInt(a);return *this;}
OUT& operator<<(float a){putDouble(a);return *this;}
OUT& operator<<(double a){putDouble(a);return *this;}
OUT& operator<<(long double a){putDouble(a);return *this;}
~OUT(){flush();}
};
}
fastio::IN fin;
fastio::OUT fout;
int sg[100010];
int mex(const vector<int>& dat){
unordered_map<int,int>mp;
for(auto i:dat){
mp[i]=1;
}
for(int i=0;i<1000000;++i){
if(mp[i]!=1)return i;
}
return -1;
}
i64 ttmp[127];
int dp[100010][128][3];
long long n,m,res;
int main(){
n=100000;
for(int i=1;i<=n;++i){
vector<int>vc;
for(int j=1;;++j){
int tmp=i-j*j;
if(tmp<0)break;
else vc.push_back(sg[tmp]);
}
sg[i]=mex(vc);
res=max(res,(i64)sg[i]);
}
for(int i=0;i<=n;++i){
dp[i][sg[i]][0]++;
}
for(int i=0;i<=n;++i){
for(int j=0;j<=127;++j){
ttmp[j]+=dp[i][j][0];
}
for(int j=0;j<=127;++j){
dp[i][j][1]+=ttmp[j^sg[i]];
}
}
for(int i=0;i<=127;++i){
ttmp[i]=0;
}
for(int i=0;i<=n;++i){
for(int j=0;j<=127;++j){
ttmp[j]+=dp[i][j][1];
}
for(int j=0;j<=127;++j){
dp[i][j][2]+=ttmp[j^sg[i]];
}
}
res=0;
for(int i=0;i<=n;++i){
res+=dp[i][0][2];
}
fout<<res;
return 0;
}
|
