Given is an integer N. How many permutations (P_0,P_1,\cdots,P_{2N-1}) of (0,1,\cdots,2N-1) satisfy the following condition?

* For each i (0 \leq i \leq 2N-1), N^2 \leq i^2+P_i^2 \leq (2N)^2 holds.



Since the number can be enormous, compute it modulo M.

Constraints

* 1 \leq N \leq 250
* 2 \leq M \leq 10^9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N M


Output

Print the number of permutations that satisfy the condition, modulo M.

Examples

Input

2 998244353


Output

4


Input

10 998244353


Output

53999264


Input

200 998244353


Output

112633322
/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author majk
 */

#ifndef MAJK_LIB
#define MAJK_LIB

#include <vector>
#include <stack>
#include <iostream>
#include <unordered_map>
#include <unordered_set>
#include <map>
#include <iomanip>
#include <set>
#include <functional>
#include <algorithm>
#include <numeric>
#include <cassert>
#include <cmath>
#include <string>
#include <queue>
#include <array>
#include <bitset>
using namespace std;

#define x first
#define y second
typedef std::pair<int,int> pii; typedef long long ll; typedef unsigned long long ull; typedef unsigned int ui; typedef pair<ui,ui> puu;

template <typename T, typename U> std::istream&operator>>(std::istream&i, pair<T,U>&p) {i >> p.x >> p.y; return i;}
template<typename T>std::istream&operator>>(std::istream&i,vector<T>&t) {for(auto&v:t){i>>v;}return i;}
template <typename T, typename U> std::ostream&operator<<(std::ostream&o, const pair<T,U>&p) {o << p.x << ' ' << p.y; return o;}
template<typename T>std::ostream&operator<<(std::ostream&o,const vector<T>&t) {if(t.empty())o<<'\n';for(size_t i=0;i<t.size();++i){o<<t[i]<<" \n"[i == t.size()-1];}return o;}
template<typename T> using minheap = priority_queue<T, vector<T>, greater<T>>;
template<typename T> using maxheap = priority_queue<T, vector<T>, less<T>>;
ui logceil(ll x) { return x?8*sizeof(ll)-__builtin_clzll(x):0; }

namespace std { template<typename T,typename U>struct hash<pair<T,U>>{hash<T>t;hash<U>u;size_t operator()(const pair<T,U>&p)const{return t(p.x)^(u(p.y)<<7);}}; }
template<typename T,typename F>T bsh(T l,T h,const F&f){T r=-1,m;while(l<=h){m=(l+h)/2;if(f(m)){l=m+1;r=m;}else{h=m-1;}}return r;}
template<typename F> double bshd(double l,double h,const F&f,double p=1e-9){ui r=3+(ui)log2((h-l)/p);while(r--){double m=(l+h)/2;if(f(m)){l=m;}else{h=m;}}return (l+h)/2;}
template<typename T,typename F>T bsl(T l,T h,const F&f){T r=-1,m;while(l<=h){m=(l+h)/2;if(f(m)){h=m-1;r=m;}else{l=m+1;}}return r;}
template<typename F> double bsld(double l,double h,const F&f,double p=1e-9){ui r=3+(ui)log2((h-l)/p);while(r--){double m=(l+h)/2;if(f(m)){h=m;}else{l=m;}}return (l+h)/2;}
template<typename T> T gcd(T a,T b) { if (a<b) swap(a,b); return b?gcd(b,a%b):a; }


template<typename T>class vector2:public vector<vector<T>>{public:vector2(){} vector2(size_t a,size_t b,T t=T()):vector<vector<T>>(a,vector<T>(b,t)){}};
template<typename T>class vector3:public vector<vector2<T>>{public:vector3(){} vector3(size_t a,size_t b,size_t c,T t=T()):vector<vector2<T>>(a,vector2<T>(b,c,t)){}};
template<typename T>class vector4:public vector<vector3<T>>{public:vector4(){} vector4(size_t a,size_t b,size_t c,size_t d,T t=T()):vector<vector3<T>>(a,vector3<T>(b,c,d,t)){}};
template<typename T>class vector5:public vector<vector4<T>>{public:vector5(){} vector5(size_t a,size_t b,size_t c,size_t d,size_t e,T t=T()):vector<vector4<T>>(a,vector4<T>(b,c,d,e,t)){}};


#endif
int MOD;

class RField {
    typedef unsigned int ui;
    typedef unsigned long long ull;
    inline int pow(int a, ll p){ui r=1,e=a;while(p){if(p&1){r=((ull)r*e)%MOD;}e=((ull)e*e)%MOD;p>>=1;}return r;}
    /*extended GCD(slow):ll t=0,nt=1,r=MOD,nr=a;while(nr){ll q=r/nr;t-=q*nt;swap(t,nt);r-=q*nr;swap(r,nr);}assert(r<=1);return(t<0)?t+MOD:t;*/
//    inline int inv(int a){return pow(a,MOD-2);}
public:
    inline RField(int x = 0) : v(x) {}
    inline RField pow(int p){return (*this)^p; }
    inline RField operator^(ll p){return {pow(v,p)};}
    inline RField&operator+=(const RField&o) {checkMod(o);if ((ll)v+o.v >= MOD) v = (ll)v+o.v-MOD; else v = v+o.v; return *this; }
    inline RField&operator-=(const RField&o) {checkMod(o);if (v<o.v) v = MOD-o.v+v; else v=v-o.v; return *this; }
    inline RField&operator*=(const RField&o) {checkMod(o);v=ll(v)*o.v % MOD; return *this; }
//    inline RField&operator/=(const RField&o) {checkMod(o); return *this*={inv(o.v),MOD}; }
    inline RField operator+(const RField&o) const {RField r{*this};return r+=o;}
    inline RField operator-(const RField&o) const {RField r{*this};return r-=o;}
    inline RField operator*(const RField&o) const {RField r{*this};return r*=o;}
//    inline RField operator/(const RField&o) const {RField r{*this};return r/=o;}
    inline RField operator-() {if(v) return {MOD-v}; else return {0};};
    inline RField& operator++() { ++v; if (v==MOD) v=0; return *this; }
    inline RField operator++(int) { RField r{*this}; ++*this; return r; }
    inline RField& operator--() { --v; if (v==-1) v=MOD-1; return *this; }
    inline RField operator--(int) { RField r{*this}; --*this; return r; }
    inline bool operator==(const RField&o) const { return o.v==v; }
    inline bool operator!=(const RField&o) const { return o.v!=v; }
    inline explicit operator int() const { return v; }
    void checkMod(const RField&o) {}
//    inline static vector<RField>fact(int t){vector<RField>F(t+1,1);for(int i=2;i<=t;++i){F[i]=F[i-1]*i;}return F;}
//    inline static vector<RField>invfact(int t){vector<RField>F(t+1,1);RField X{1};for(int i=2;i<=t;++i){X=X*i;}F[t]=1/X;for(int i=t-1;i>=2;--i){F[i]=F[i+1]*(i+1);}return F;}
private:
    int v;
};
//istream &operator>>(std::istream&is,RField&f){unsigned int v;is>>v;f=v;return is;}
ostream &operator<<(std::ostream&os,const RField&f){return os<<int(f);}
RField operator+(int i,const RField&f){return i+f;}
RField operator-(int i,const RField&f){return i-f;}
RField operator*(int i,const RField&f){return i*f;}
RField operator/(int i,const RField&f){return i/f;}


class FSquareConstraints {
public:
    void solve(istream& cin, ostream& cout) {
        int N, M; cin >> N >> M;
        vector<int> LO(2*N, 2*N), HI(2*N, 0);
        for (int i = 0; i < 2*N; ++i) {
            for (int j = 0; j < 2*N; ++j) {
                if (i*i + j*j <= 4*N*N && i*i + j*j >= N*N) {
                    LO[i] = min(LO[i], j-1);
                    HI[i] = max(HI[i], j);
                }
            }
        }

//        cout << LO << HI;

        vector<pii> X;
        for (int i = 0; i < N; ++i) X.push_back({LO[i], -i});
        for (int i = N; i < 2*N; ++i) X.push_back({HI[i], -i});
        sort(X.begin(),X.end());

//        cout << X;

        MOD = M;
        RField ans = 0;
        for (int K = 0; K <= N; ++K) {
            vector2<RField> D(2*N+1, K+1, 0);
            D[0][0] = 1;
            int left = 0;
            for (int i = 0; i < 2*N; ++i) {
                int y = -X[i].y;
                int right = i - left;
                for (int j = 0; j <= K; ++j) {
                    int lo = j;
                    int hi = left - j;

                    if (y >= N) {
                        D[i+1][j] += D[i][j] * max(0, 1 + X[i].x - (lo+right));
                    } else {
                        if (j != K) {
                            D[i+1][j+1] += D[i][j] * max(0, 1 + X[i].x - (lo+right));
                        }

//                        if (K == 0) {
//                            cout << HI[X[i].y] << ' ' << hi << endl;
//                        }
                        D[i+1][j] += D[i][j] * max(0, 1 + HI[y] - (N+K+hi));
                    }
                }
                left += y < N;
            }

//            cout << D;
//            cout << D[2*N][K] << endl;
            if (K%2 == 0) {
                ans += D[2*N][K];
            } else {
                ans -= D[2*N][K];
            }
        }

        cout << ans << endl;

    }
};


int main() {
	ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr);
	FSquareConstraints solver;
	std::istream& in(std::cin);
	std::ostream& out(std::cout);
	solver.solve(in, out);
    return 0;
}
