#include using namespace std; using ll = long long; using ld = long double; using ull = unsigned long long; using uint = unsigned; using pcc = pair; using pii = pair; using pll = pair; using pdd = pair; using tuplis = array; template using pq = priority_queue, greater>; const ll LINF=0x1fffffffffffffff; const ll MINF=0x7fffffffffff; const int INF=0x3fffffff; const int MOD=1000000007; const int MODD=998244353; const ld DINF=numeric_limits::infinity(); const ld EPS=1e-9; const ld PI=3.1415926535897932; const ll dx[] = {0, 1, 0, -1, 1, -1, 1, -1}; const ll dy[] = {1, 0, -1, 0, 1, 1, -1, -1}; #define overload4(_1,_2,_3,_4,name,...) name #define overload3(_1,_2,_3,name,...) name #define rep1(n) for(ll i=0;i(a);) #define rrep4(i,a,b,c) for(ll i=a+(b-a-1)/c*c;i>=a;i-=c) #define rrep(...) overload4(__VA_ARGS__,rrep4,rrep3,rrep2,rrep1)(__VA_ARGS__) #define each1(i,a) for(auto&& i:a) #define each2(x,y,a) for(auto&& [x,y]:a) #define each3(x,y,z,a) for(auto&& [x,y,z]:a) #define each(...) overload4(__VA_ARGS__,each3,each2,each1)(__VA_ARGS__) #define all1(i) begin(i),end(i) #define all2(i,a) begin(i),begin(i)+a #define all3(i,a,b) begin(i)+a,begin(i)+b #define all(...) overload3(__VA_ARGS__,all3,all2,all1)(__VA_ARGS__) #define rall1(i) (i).rbegin(),(i).rend() #define rall2(i,k) (i).rbegin(),(i).rbegin()+k #define rall3(i,a,b) (i).rbegin()+a,(i).rbegin()+b #define rall(...) overload3(__VA_ARGS__,rall3,rall2,rall1)(__VA_ARGS__) #define sum(...) accumulate(all(__VA_ARGS__),0LL) #define dsum(...) accumulate(all(__VA_ARGS__),0.0L) #define elif else if #define unless(a) if(!(a)) #define mp make_pair #define mt make_tuple #define INT(...) int __VA_ARGS__;in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;in(__VA_ARGS__) #define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__) #define STR(...) string __VA_ARGS__;in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__;in(__VA_ARGS__) #define Sort(a) sort(all(a)) #define Rev(a) reverse(all(a)) #define Uniq(a) sort(all(a));a.erase(unique(all(a)),end(a)) #define vec(type,name,...) vector name(__VA_ARGS__) #define VEC(type,name,size) vector name(size);in(name) #define vv(type,name,h,...) vector>name(h,vector(__VA_ARGS__)) #define VV(type,name,h,w) vector>name(h,vector(w));in(name) #define vvv(type,name,h,w,...) vector>>name(h,vector>(w,vector(__VA_ARGS__))) template auto min(const T& a){ return *min_element(all(a)); } template auto max(const T& a){ return *max_element(all(a)); } inline ll popcnt(ull a){ return __builtin_popcountll(a); } ll gcd(ll a, ll b){ while(b){ ll c = b; b = a % b; a = c; } return a; } ll lcm(ll a, ll b){ if(!a || !b) return 0; return a * b / gcd(a, b); } ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; } ll modpow(ll a, ll b, ll p){ ll ans = 1; while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; } template bool chmin(T& a, const U& b){ if(a > b){ a = b; return 1; } return 0; } template bool chmax(T& a, const U& b){ if(a < b){ a = b; return 1; } return 0; } vector iota(ll n){ vector a(n); iota(a.begin(), a.end(), 0); return a; } vector factor(ull x){ vector ans; for(ull i = 2; i * i <= x; i++) if(x % i == 0){ ans.push_back({i, 1}); while((x /= i) % i == 0) ans.back().second++; } if(x != 1) ans.push_back({x, 1}); return ans; } map factor_map(ull x){ map ans; for(ull i = 2; i * i <= x; i++) if(x % i == 0){ ans[i] = 1; while((x /= i) % i == 0) ans[i]++; } if(x != 1) ans[x] = 1; return ans; } vector divisor(ull x){ vector ans; for(ull i = 1; i * i <= x; i++) if(x % i == 0) ans.push_back(i); rrep(ans.size() - (ans.back() * ans.back() == x)) ans.push_back(x / ans[i]); return ans; } template unordered_map press(vector& a){ auto b = a; sort(all(b)); b.erase(unique(all(b)), b.end()); unordered_map ans; rep(b.size()) ans[b[i]] = i; each(i, a) i = ans[i]; return ans; } template map press_map(vector& a){ auto b = a; sort(all(b)); b.erase(unique(all(b)), b.end()); map ans; rep(b.size()) ans[b[i]] = i; each(i, a) i = ans[i]; return ans; } int scan(){ return getchar(); } void scan(int& a){ scanf("%d", &a); } void scan(unsigned& a){ scanf("%u", &a); } void scan(long& a){ scanf("%ld", &a); } void scan(long long& a){ scanf("%lld", &a); } void scan(unsigned long long& a){ scanf("%llu", &a); } void scan(char& a){ do{ a = getchar(); }while(a == ' ' || a == '\n'); } void scan(float& a){ scanf("%f", &a); } void scan(double& a){ scanf("%lf", &a); } void scan(long double& a){ scanf("%Lf", &a); } void scan(vector& a){ for(unsigned i = 0; i < a.size(); i++){ int b; scan(b); a[i] = b; } } void scan(char a[]){ scanf("%s", a); } void scan(string& a){ cin >> a; } template void scan(vector&); template void scan(array&); template void scan(pair&); template void scan(T(&)[size]); template void scan(vector& a){ for(auto&& i : a) scan(i); } template void scan(deque& a){ for(auto&& i : a) scan(i); } template void scan(array& a){ for(auto&& i : a) scan(i); } template void scan(pair& p){ scan(p.first); scan(p.second); } template void scan(T (&a)[size]){ for(auto&& i : a) scan(i); } template void scan(T& a){ cin >> a; } void in(){} template void in(Head& head, Tail&... tail){ scan(head); in(tail...); } void print(){ putchar(' '); } void print(bool a){ printf("%d", a); } void print(int a){ printf("%d", a); } void print(unsigned a){ printf("%u", a); } void print(long a){ printf("%ld", a); } void print(long long a){ printf("%lld", a); } void print(unsigned long long a){ printf("%llu", a); } void print(char a){ printf("%c", a); } void print(char a[]){ printf("%s", a); } void print(const char a[]){ printf("%s", a); } void print(float a){ printf("%.15f", a); } void print(double a){ printf("%.15f", a); } void print(long double a){ printf("%.15Lf", a); } void print(const string& a){ for(auto&& i : a) print(i); } template void print(const vector&); template void print(const array&); template void print(const pair& p); template void print(const T (&)[size]); template void print(const vector& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } } template void print(const deque& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } } template void print(const array& a){ print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } } template void print(const pair& p){ print(p.first); putchar(' '); print(p.second); } template void print(const T (&a)[size]){ print(a[0]); for(auto i = a; ++i != end(a); ){ putchar(' '); print(*i); } } template void print(const T& a){ cout << a; } int out(){ putchar('\n'); return 0; } template int out(const T& t){ print(t); putchar('\n'); return 0; } template int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; } #ifdef DEBUG inline ll __lg(ull __n){ return sizeof(ull) * __CHAR_BIT__ - 1 - __builtin_clzll(__n); } #define debug(...) { print(#__VA_ARGS__); print(":"); out(__VA_ARGS__); } #else #define debug(...) void(0) #endif int first(bool i = true){ return out(i?"first":"second"); } int yes(bool i = true){ return out(i?"yes":"no"); } int Yes(bool i = true){ return out(i?"Yes":"No"); } int No(){ return out("No"); } int YES(bool i = true){ return out(i?"YES":"NO"); } int NO(){ return out("NO"); } int Yay(bool i = true){ return out(i?"Yay!":":("); } int possible(bool i = true){ return out(i?"possible":"impossible"); } int Possible(bool i = true){ return out(i?"Possible":"Impossible"); } int POSSIBLE(bool i = true){ return out(i?"POSSIBLE":"IMPOSSIBLE"); } void Case(ll i){ printf("Case #%lld: ", i); } constexpr uint mod = MOD; struct Modint{ uint num = 0; constexpr Modint() noexcept {} constexpr Modint(const Modint &x) noexcept : num(x.num){} inline constexpr operator ll() const noexcept { return num; } inline constexpr Modint& operator+=(Modint x) noexcept { num += x.num; if(num >= mod) num -= mod; return *this; } inline constexpr Modint& operator++() noexcept { if(num == mod - 1) num = 0; else num++; return *this; } inline constexpr Modint operator++(int) noexcept { Modint ans(*this); operator++(); return ans; } inline constexpr Modint operator-() const noexcept { return Modint(0) -= *this; } inline constexpr Modint operator-(Modint x) const noexcept { return Modint(*this) -= x; } inline constexpr Modint& operator-=(Modint x) noexcept { if(num < x.num) num += mod; num -= x.num; return *this; } inline constexpr Modint& operator--() noexcept { if(num == 0) num = mod - 1; else num--; return *this; } inline constexpr Modint operator--(int) noexcept { Modint ans(*this); operator--(); return ans; } inline constexpr Modint& operator*=(Modint x) noexcept { num = ull(num) * x.num % mod; return *this; } inline constexpr Modint& operator/=(Modint x) noexcept { return operator*=(x.inv()); } template constexpr Modint(T x) noexcept { using U = typename conditional= 4, T, int>::type; U y = x; y %= U(mod); if(y < 0) y += mod; num = uint(y); } template inline constexpr Modint operator+(T x) const noexcept { return Modint(*this) += x; } template inline constexpr Modint& operator+=(T x) noexcept { return operator+=(Modint(x)); } template inline constexpr Modint operator-(T x) const noexcept { return Modint(*this) -= x; } template inline constexpr Modint& operator-=(T x) noexcept { return operator-=(Modint(x)); } template inline constexpr Modint operator*(T x) const noexcept { return Modint(*this) *= x; } template inline constexpr Modint& operator*=(T x) noexcept { return operator*=(Modint(x)); } template inline constexpr Modint operator/(T x) const noexcept { return Modint(*this) /= x; } template inline constexpr Modint& operator/=(T x) noexcept { return operator/=(Modint(x)); } inline constexpr Modint inv() const noexcept { ll x = 0, y = 0; extgcd(num, mod, x, y); return x; } static inline constexpr ll extgcd(ll a, ll b, ll &x, ll &y) noexcept { ll g = a; x = 1; y = 0; if(b){ g = extgcd(b, a % b, y, x); y -= a / b * x; } return g; } inline constexpr Modint pow(ull x) const noexcept { Modint ans = 1, cnt = *this; while(x){ if(x & 1) ans *= cnt; cnt *= cnt; x /= 2; } return ans; } }; std::istream& operator>>(std::istream& is, Modint& x){ ll a; in(a); x = a; return is; } inline constexpr Modint operator""_M(ull x) noexcept { return Modint(x); } std::vector fac(1, 1), inv(1, 1); inline void reserve(ll a){ if(fac.size() >= a) return; if(a < fac.size() * 2) a = fac.size() * 2; if(a >= mod) a = mod; while(fac.size() < a) fac.push_back(fac.back() * Modint(fac.size())); inv.resize(fac.size()); inv.back() = fac.back().inv(); for(ll i = inv.size() - 1; !inv[i - 1]; i--) inv[i - 1] = inv[i] * i; } inline Modint fact(ll n){ if(n < 0) return 0; reserve(n + 1); return fac[n]; } inline Modint perm(ll n, ll r){ if(r < 0 || n < r) return 0; if(n >> 24){ Modint ans = 1; for(ll i = 0; i < r; i++) ans *= n--; return ans; } reserve(n + 1); return fac[n] * inv[n - r]; } inline Modint comb(ll n, ll r){ if(r < 0 || n < r) return 0; reserve(r + 1); return perm(n, r) * inv[r]; } inline Modint Mcomb(ll n, ll r){ return comb(n + r - 1, n - 1); } // r balls into n boxes inline Modint catalan(ll n){ reserve(n * 2 + 1); return fac[n * 2] * inv[n] * inv[n + 1]; } struct UnWeightedEdge{ ll to; static constexpr ll cost = 1; UnWeightedEdge(){} UnWeightedEdge(ll to): to(to){} operator ll() const { return to; } }; signed main(){ LL(n); vec(Modint,a,n); vec(ll,parent,n,-1); vec(vector,child,n); rep(n-1){ LL(a,b); a--; b--; parent[b]=a; child[a].push_back(b); } ll root=0; while(parent[root]!=-1)root=parent[root]; vec(Modint,dist,n); vec(Modint,up,n); vec(Modint,down,n); auto dfs=[&](ll at,const auto&dfs)->void{ each(i,child[at]){ dist[i]=dist[at]+1; up[i]=up[at]+1; dfs(i,dfs); } }; dfs(root,dfs); auto dfs2=[&](ll at,const auto&dfs)->void{ each(i,child[at]){ dfs(i,dfs); down[at]+=down[i]+1; } }; dfs2(root,dfs2); Modint ans=0; rep(n)ans+=dist[i]*(up[i]-down[i]); out(ans); }