#pragma GCC optimize("Ofast")
// #pragma GCC optimize("unroll-loops")
// #pragma GCC push_options
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include<bits/stdc++.h>
#include <xmmintrin.h>
#include <immintrin.h>
using namespace::std;
__attribute__((constructor))void init(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(15);}
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/priority_queue.hpp>
#include<ext/pb_ds/tag_and_trait.hpp>
// #include <boost/multiprecision/cpp_dec_float.hpp>
// #include <boost/multiprecision/cpp_int.hpp>
// namespace mp = boost::multiprecision;
// typedef mp::number<mp::cpp_dec_float<0>> cdouble;
// typedef mp::cpp_int cint;
template<typename T>using pbds=__gnu_pbds::tree<T,__gnu_pbds::null_type,less<T>,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>;
template<typename T>using pbds_map=__gnu_pbds::tree<T,T,less<T>,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>;
template<typename T,typename E>using hash_map=__gnu_pbds::gp_hash_table<T,E>;
template<typename T>using pqueue =__gnu_pbds::priority_queue<T, greater<T>,__gnu_pbds::rc_binomial_heap_tag>;
typedef long long lint;
#define INF (1LL<<60)
#define IINF (1<<30)
#define EPS (1e-10)
#define MOD 1000000007LL
//#define MOD 998244353LL
typedef vector<lint> vec;
typedef vector<vector<lint>> mat;
typedef vector<vector<vector<lint>>> mat3;
typedef vector<string> svec;
typedef vector<vector<string>> smat;
template<typename T>inline void numout(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<<i<INF/2?i:"INF";f=1;}cout<<endl;}
template<typename T>inline void numout2(T t){for(auto i:t)numout(i);}
template<typename T>inline void output(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<<i;f=1;}cout<<endl;}
template<typename T>inline void output2(T t){for(auto i:t)output(i);}
template<typename T>inline void _output(T t){bool f=0;for(lint i=0;i<t.size();i++){cout<<f?"":" "<<t[i];f=1;}cout<<endl;}
template<typename T>inline void _output2(T t){for(lint i=0;i<t.size();i++)output(t[i]);}
#define rep(i,n) for(lint i=0;i<lint(n);++i)
#define repi(i,a,b) for(lint i=lint(a);i<(lint)(b);++i)
#define rrep(i,n) for(lint i=lint(n)-1;i>=0;--i)
#define rrepi(i,a,b) for(lint i=lint(b)-1;i>=lint(a);--i)
#define irep(i) for(lint i=0;;++i)
#define all(n) begin(n),end(n)
#define dist(a,b,c,d) sqrt(pow(a-c,2)+pow(b-d,2))
inline lint gcd(lint A,lint B){return B?gcd(B,A%B):A;}
inline lint lcm(lint A,lint B){return A/gcd(A,B)*B;}
// inline cint cgcd(cint A,cint B){return B?cgcd(B,A%B):A;}
// inline cint clcm(cint A,cint B){return A/cgcd(A,B)*B;}
inline bool chmin(auto& s,const auto& t){bool res=s>t;s=min(s,t);return res;}
inline bool chmax(auto& s,const auto& t){bool res=s<t;s=max(s,t);return res;}
const vector<lint> dx={1,0,-1,0,1,1,-1,-1};
const vector<lint> dy={0,1,0,-1,1,-1,1,-1};
#define SUM(v) accumulate(all(v),0LL)
//auto call=[&](auto f,auto... args){return f(f,args...);};

template<typename T,typename P>
struct FPS_BASE:vector<T>{
    using vector<T>::vector;
    P operator +(T x){return P(*dynamic_cast<P*>(this))+=x;}
    P operator -(T x){return P(*dynamic_cast<P*>(this))-=x;}
    P operator *(T x){return P(*dynamic_cast<P*>(this))*=x;}
    P operator /(T x){return P(*dynamic_cast<P*>(this))/=x;}
    P operator <<(int x){return P(*dynamic_cast<P*>(this))<<=x;}
    P operator >>(int x){return P(*dynamic_cast<P*>(this))>>=x;}
    P operator +(P x){return P(*dynamic_cast<P*>(this))+=x;}
    P operator -(P x){return P(*dynamic_cast<P*>(this))-=x;}
    P operator -(){return P(1,T(0))-=P(*dynamic_cast<P*>(this));}
    P operator *(P x){return P(*dynamic_cast<P*>(this))*=x;}
    P operator /(P x){return P(*dynamic_cast<P*>(this))/=x;}
    P operator %(P x){return P(*dynamic_cast<P*>(this))%=x;}
    P &operator +=(T x){
        if(this->size()==0)this->resize(1,T(0));
        (*dynamic_cast<P*>(this))[0]+=x;
        return (*dynamic_cast<P*>(this));
    }
    P &operator -=(T x){
        if(this->size()==0)this->resize(1,T(0));
        (*dynamic_cast<P*>(this))[0]-=x;
        return (*dynamic_cast<P*>(this));
    }
    P &operator *=(T x){
        for(int i=0;i<(int)this->size();++i){
            (*dynamic_cast<P*>(this))[0]*=x;
        }
        return (*dynamic_cast<P*>(this));
    }
    P &operator /=(T x){
        for(int i=0;i<(int)this->size();++i){
            (*dynamic_cast<P*>(this))[0]/=x;
        }
        return (*dynamic_cast<P*>(this));
    }
    P &operator <<=(int x){
        P ret(x,T(0));
        ret.insert(ret.end(),begin(*dynamic_cast<P*>(this)),end(*dynamic_cast<P*>(this)));
        return (*dynamic_cast<P*>(this))=ret;
    }
    P &operator >>=(int x){
        P ret;
        ret.insert(ret.end(),begin(*dynamic_cast<P*>(this))+x,end(*dynamic_cast<P*>(this)));
        return (*dynamic_cast<P*>(this))=ret;
    }
    P &operator +=(P x){
        if(this->size()<x.size())this->resize(x.size(),T(0));
        for(int i=0;i<(int)x.size();++i){
            (*dynamic_cast<P*>(this))[i]+=x[i];
        }
        return (*dynamic_cast<P*>(this));
    }
    P &operator -=(P x){
        if(this->size()<x.size())this->resize(x.size(),T(0));
        for(int i=0;i<(int)x.size();++i){
            (*dynamic_cast<P*>(this))[i]-=x[i];
        }
        return (*dynamic_cast<P*>(this));
    }
    P &operator *=(P x){
        return (*dynamic_cast<P*>(this))=mul((*dynamic_cast<P*>(this)),x);
    }
    P &operator /=(P x){
        if(this->size()<x.size()) {
            this->clear();
            return (*dynamic_cast<P*>(this));
        }
        const int n=x.size()-this->size()+1;
        return (*dynamic_cast<P*>(this)) = (rev().pre(n)*x.rev().inv(n)).pre(n).rev(n);
    }
    P &operator %=(P x){
        return (*dynamic_cast<P*>(this))-(*dynamic_cast<P*>(this))/x*x;
    }
    P& shrink(){while((*dynamic_cast<P*>(this)).back()==0)(*dynamic_cast<P*>(this)).pop_back();return (*dynamic_cast<P*>(this));}
    P pre(int sz)const{
        return P(begin(*this),begin(*this)+min((int)this->size(),sz));
    }
    P rev(int deg=-1){
        P ret(*dynamic_cast<P*>(this));
        if(deg!=-1)ret.resize(deg,T(0));
        reverse(begin(ret),end(ret));
        return ret;
    }
    P inv(int deg=-1){
        assert((*dynamic_cast<P*>(this))[0]!=T(0));
        const int n=deg==-1?this->size():deg;
        P ret({T(1)/(*this)[0]});
        for(int i=1;i<n;i<<=1){
            ret=ret*(-ret*pre(i<<1)+2).pre(i<<1);
        }
        return ret.pre(n);
    }
    P dot(P x){
        P ret(*dynamic_cast<P*>(this));
        for(int i=0;i<int(min(this->size(),x.size()));++i){
            ret[i]*=x[i];
        }
        return ret;
    }
    P diff(){
        P ret(*dynamic_cast<P*>(this));
        for(int i=0;i<(int)ret.size();i++){
            ret[i]*=i;
        }
        return ret>>1;
    }
    P integral(){
        P ret(*dynamic_cast<P*>(this));
        for(int i=0;i<(int)ret.size();i++){
            ret[i]/=i+1;
        }
        return ret<<1;
    }
    P log(int deg=-1){
        assert((*this)[0]==T(1));
        const int n=deg==-1?this->size():deg;
        return (diff()*inv(n)).pre(n-1).integral();
    }
    P exp(int deg=-1){
        assert((*this)[0]==T(0));
        const int n=deg==-1?this->size():deg;
        P ret({T(1)});
        for(int i=1;i<n;i<<=1){
            ret=ret*(pre(i<<1)+1-ret.log(i<<1)).pre(i<<1);
        }
        return ret.pre(n);
    }
    P sqrt(int deg=-1){
        const int n=deg==-1?this->size():deg;
        if((*this)[0]==T(0)) {
            for(int i=1;i<(int)this->size();i++) {
                if((*this)[i]!=T(0)) {
                    if(i&1)return{};
                    if(n-i/2<=0)break;
                    auto ret=(*this>>i).sqrt(n-i/2)<<(i/2);
                    if((int)ret.size()<n)ret.resize(n,T(0));
                    return ret;
                }
            }
            return P(n,0);
        }
        P ret({T(1)});
        for(int i=1;i<n;i<<=1){
            ret=(ret+pre(i<<1)*ret.inv(i<<1)).pre(i<<1)/T(2);
        }
        return ret.pre(n);
    }
    virtual P mul(P s,P t)=0;
};

template<typename Mint>
struct fps1:FPS_BASE<Mint,fps1<Mint>>{
    class mint_fps;
    using FPS_BASE<Mint,fps1<Mint>>::FPS_BASE;
    using P=fps1<Mint>;
    P mul(P s,P t)override{
        lint n=s.size()+t.size()-1;
        lint h=1;
        while((1<<h)<n)h++;
        vector<mint_fps>a(1<<h,mint_fps(0)),b(1<<h,mint_fps(0));
        for(int i=0;i<(int)s.size();i++){
            a[i]=s[i].value();
        }
        for(int i=0;i<(int)t.size();i++){
            b[i]=t[i].value();
        }
        auto c=ntt(a,h,0);
        auto d=ntt(b,h,0);
        for(int i=0;i<(1<<h);i++){
            c[i]*=d[i];
        }
        auto tmp=ntt(c,h,1);
        P res(n);
        for(int i=0;i<n;i++)res[i]=tmp[i].value();
        return res.pre(n);
    }
    vector<mint_fps> ntt(vector<mint_fps> v,const int& h,const bool& inv){
		int n=v.size(),mask=n-1;
		vector<mint_fps> tmp(n);
        vector<mint_fps> table(n,1);
        mint_fps theta=mint_fps(3).base(h);
        if(inv)theta=theta.inv();
        for(int i=1;i<n;++i)table[i]=table[i-1]*theta;
        for(int j=n>>1,t=h-1;j>=1;j>>=1,--t){
            for(int k=0;k<n;++k){
                int s=k&(j-1);
                int i=k>>t;
                tmp[k]=v[((i<<(t+1))|s)&mask]+table[i*j]*v[((i<<(t+1))|j|s)&mask];
            }
            swap(v,tmp);
        }
        if(inv)for(int i=0;i<n;++i)v[i]/=n;
        return v;
	}
    class mint_fps{
        using u64 = std::uint_fast64_t;
        u64 mods[3]={1224736769,1045430273,1007681537};
        public:
        u64 a[3];
        constexpr mint_fps(const long long x = 0){
            for(int i=0;i<3;i++){
                a[i]=x>=0?x%get_mod():get_mod()-(-x)%get_mod();
            }
        }
        constexpr u64 value() noexcept {
            return garner();
        }
        constexpr mint_fps operator+(const mint_fps rhs)const noexcept{return mint_fps(*this) += rhs;}
        constexpr mint_fps operator-(const mint_fps rhs)const noexcept{return mint_fps(*this)-=rhs;}
        constexpr mint_fps operator*(const mint_fps rhs) const noexcept {return mint_fps(*this) *= rhs;}
        constexpr mint_fps operator/(const mint_fps rhs) const noexcept {return mint_fps(*this) /= rhs;}
        constexpr mint_fps &operator+=(const mint_fps rhs) noexcept {
            for(int i=0;i<3;++i){
                a[i]+=rhs.a[i];
                if (a[i]>=mods[i])a[i]-=mods[i];
            }
            return *this;
        }
        constexpr bool operator==(mint_fps x) noexcept {
            return a==x.a;
        }
        constexpr bool operator!=(mint_fps x) noexcept {
            return a!=x.a;
        }
        constexpr mint_fps &operator-=(const mint_fps rhs) noexcept {
            for(int i=0;i<3;++i){
                a[i]-=rhs.a[i];
                if (a[i]>=mods[i])a[i]-=mods[i];
            }
            return *this;
        }
        constexpr mint_fps &operator*=(const mint_fps rhs) noexcept {
            for(int i=0;i<3;++i){
                a[i]=a[i]*rhs.a[i]%mods[i];
            }
            return *this;
        }
        constexpr mint_fps &operator/=(mint_fps rhs)noexcept{
            for(int i=0;i<3;i++){
                u64 ret =rhs.a[i];
                u64 exp=mods[i]-2;
                while (exp) {
                    if (exp %2) {
                        (a[i]*=ret)%=mods[i];
                    }
                    (ret *= ret)%=mods[i];
                    exp /= 2;
                }
            }
            return *this;
        }
        constexpr mint_fps operator++(int n) noexcept {
            return *this+=1;
        }
        constexpr mint_fps operator--(int n) noexcept {
            return *this-=1;
        }
        constexpr mint_fps base(int h)noexcept{
            for(int i=0;i<3;i++){
                u64 ret =3;
                a[i]=1;
                u64 exp=((mods[i]-1)>>h);
                while (exp) {
                    if (exp %2) {
                        (a[i]*=ret)%=mods[i];
                    }
                    (ret *= ret)%=mods[i];
                    exp /= 2;
                }
            }
            return *this;
        }
        constexpr mint_fps inv(){
            return mint_fps(1)/(*this);
        }
        constexpr static u64 get_mod(){return MOD;}
        constexpr u64 garner(){
            const int sz=3;
            using u64 = long long;
            const u64 mods[4]={1224736769,1045430273,1007681537,get_mod()};
            u64 coeffs[sz+1]={1,1,1,1};
            u64 constants[sz+1]={};
            auto modinv=[](u64 x,u64 mod){
                u64 y=mod-2;
                u64 ret=1;
                while(y>0) {
                    if(y&1)(ret*=x)%=mod;
                    (x*=x)%=mod;
                    y>>=1;
                }
                return ret;
            };
            for(int i=0;i<sz;i++) {
                u64 v=(mods[i]+a[i]-constants[i])%mods[i]*modinv(coeffs[i],mods[i])%mods[i];
                for(int j=i+1;j<sz+1;j++) {
                    constants[j]=(constants[j]+coeffs[j]*v)%mods[j];
                    coeffs[j]=(coeffs[j]*mods[i])%mods[j];
                }
            }
            return constants[3];
        }
    };
};

class mint {
  using u64 = std::uint_fast64_t;
    public:
    u64 a;
    constexpr mint(const long long x = 0)noexcept:a(x>=0?x%get_mod():get_mod()-(-x)%get_mod()){}
    constexpr u64 &value()noexcept{return a;}
    constexpr const u64 &value() const noexcept {return a;}
    constexpr mint operator+(const mint rhs)const noexcept{return mint(*this) += rhs;}
    constexpr mint operator-(const mint rhs)const noexcept{return mint(*this)-=rhs;}
    constexpr mint operator*(const mint rhs) const noexcept {return mint(*this) *= rhs;}
    constexpr mint operator/(const mint rhs) const noexcept {return mint(*this) /= rhs;}
    constexpr mint &operator+=(const mint rhs) noexcept {
        a += rhs.a;
        if (a >= get_mod())a -= get_mod();
        return *this;
    }
    constexpr mint &operator-=(const mint rhs) noexcept {
        if (a<rhs.a)a += get_mod();
        a -= rhs.a;
        return *this;
    }
    constexpr mint &operator*=(const mint rhs) noexcept {
        a = a * rhs.a % get_mod();
        return *this;
    }
    constexpr mint operator++(int n) noexcept {
        a += 1;
        if (a >= get_mod())a -= get_mod();
        return *this;
    }
    constexpr mint operator--(int n) noexcept {
        if (a<1)a += get_mod();
        a -= 1;
        return *this;
    }
    constexpr bool operator==(mint x) noexcept {
        return a==x.a;
    }
    constexpr bool operator!=(mint x) noexcept {
        return a!=x.a;
    }
    constexpr mint &operator/=(mint rhs) noexcept {
        u64 exp=get_mod()-2;
        while (exp) {
            if (exp % 2) {
                *this *= rhs;
            }
            rhs *= rhs;
            exp /= 2;
        }
        return *this;
    }
    constexpr static int root(){
        mint root = 2;
        while(root.pow((get_mod()-1)>>1).a==1)root++;
        return root.a;
    }
    constexpr mint pow(long long n){
        long long x=a;
        mint ret = 1;
        while(n>0) {
            if(n&1)(ret*=x);
            (x*=x)%=get_mod();
            n>>=1;
        }
        return ret;
    }
    constexpr mint inv(){
        return pow(get_mod()-2);
    }
    mint comb(lint b){
        using lint=long long;
        static bool init=1;
        static lint fac[3000001],ifac[3000001];
        if(init){
            init=0;
            fac[0]=1;
            ifac[0]=1;
            auto mod_pow=[&](lint x,lint n){
                lint ans = 1;
                while(n != 0){
                    if(n&1)ans=ans*x%get_mod();
                    x=x*x%get_mod();
                    n=n>>1;
                }
                return ans;
            };
            for(int i=0;i<3000000;i++){
                fac[i+1]=fac[i]*(i+1)%get_mod();
                ifac[i+1]=ifac[i]*mod_pow(i+1, get_mod()-2)%get_mod();
            }
        }
        if(a==0&&b==0)return 1;
        if((lint)a<b||a<0)return 0;
        lint tmp=ifac[a-b]*ifac[b]%get_mod();
        return tmp*fac[a]%get_mod();
    }
    
    friend ostream& operator<<(ostream& lhs, const mint& rhs) noexcept {
        lhs << rhs.a;
        return lhs;
    }
    friend istream& operator>>(istream& lhs,mint& rhs) noexcept {
        lhs >> rhs.a;
        return lhs;
    }
    constexpr static u64 get_mod(){return MOD;}
};
inline mint fact(lint a){return a?fact(a-1)*a:1;}

int main(){
    fps1<mint> c;
    lint n;
    cin>>n;
    vec a(n),b(n);
    rep(i,n){
        cin>>a[i]>>b[i];
    }
    lint mx=*max_element(all(a));
    vector<fps1<mint>> tmp(4001,fps1<mint>(mx));
    rep(i,n){
        tmp[a[i]+b[i]][mx-a[i]]++;
    }
    rrep(i,4001){
        c+=c<<1;
        c+=tmp[i];
    }
    mint ans=(c*c)[2*mx];
    rep(i,n){
        ans-=mint(2*(a[i]+b[i])).comb(a[i]*2);
    }
    cout<<ans/2<<endl;
}

Measured memory_bytes: 113412