Problem:
Score : 700 points

Problem Statement

There is a tree with N vertices, numbered 1 through N.
The i-th of the N-1 edges connects vertices a_i and b_i.

Currently, there are A_i stones placed on vertex i.
Determine whether it is possible to remove all the stones from the vertices by repeatedly performing the following operation:

Select a pair of different leaves. Then, remove exactly one stone from every vertex on the path between those two vertices.
Here, a leaf is a vertex of the tree whose degree is 1, and the selected leaves themselves are also considered as vertices on the path connecting them.

Note that the operation cannot be performed if there is a vertex with no stone on the path.

Constraints

2 ≦ N ≦ 10^5

1 ≦ a_i,b_i ≦ N

0 ≦ A_i ≦ 10^9

The given graph is a tree.

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 … A_N
a_1 b_1
:
a_{N-1} b_{N-1}

Output

If it is possible to remove all the stones from the vertices, print YES. Otherwise, print NO.

Sample Input 1

5
1 2 1 1 2
2 4
5 2
3 2
1 3

Sample Output 1

YES

All the stones can be removed, as follows:

Select vertices 4 and 5. Then, there is one stone remaining on each vertex except 4.

Select vertices 1 and 5. Then, there is no stone on any vertex.

Sample Input 2

3
1 2 1
1 2
2 3

Sample Output 2

NO

Sample Input 3

6
3 2 2 2 2 2
1 2
2 3
1 4
1 5
4 6

Sample Output 3

YES

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

//注意点
//Tは3つの値を持つ構造
//だがワイルドカードとしても使っている
//#pragma GCC optimize ("-O3")
#include <bits/stdc++.h>
using namespace std;
//@起動時
struct initon {
    initon() {
        cin.tie(0);
        ios::sync_with_stdio(false);
        cout.setf(ios::fixed);
        cout.precision(16);
        srand((unsigned) clock() + (unsigned) time(NULL));
    };
} __initon;
//衝突対策
#define ws ___ws

//@必須構造
struct T {
    int f, s, t;
    T() { f = -1, s = -1, t = -1; }
    T(int f, int s, int t) : f(f), s(s), t(t) {}
    bool operator<(const T &r) const {
        return f != r.f ? f < r.f : s != r.s ? s < r.s : t < r.t;
        //return f != r.f ? f > r.f : s != r.s ? s > r.s : t > r.t; 大きい順
    }
    bool operator>(const T &r) const {
        return f != r.f ? f > r.f : s != r.s ? s > r.s : t > r.t;
        //return f != r.f ? f > r.f : s != r.s ? s > r.s : t > r.t; 小さい順
    }
    int operator[](int i) {
        assert(i < 3);
        return i == 0 ? f : i == 1 ? s : t;
    }
};

//@マクロ省略系 型,構造

#define int long long
#define ll long long
#define double long double
#define ull unsigned long long
using dou = double;
using itn = int;
using str = string;
using bo= bool;
using P = pair<ll, ll>;
#define F first
#define fi first
#define S second
#define se second
#define vec vector
#define beg begin
#define rbeg rbegin
#define con continue
#define bre break
#define brk break
#define is ==


//マクロ省略系 コンテナ

using vi = vector<int>;
#define vvi(a, b, c) vec<vi> a(b,vi(c))
using vb = vector<bool>;
#define vvb(a, b, c) vec<vb> a(b,vb(c))
using vs = vector<string>;
#define vvs(a, b, c) vec<vs> a(b,vs(c))
using vl = vector<ll>;
#define vvl(a, b, c) vec<vl> a(b,vl(c))
using vd = vector<double>;
#define vvd(a, b, c) vec<vd> a(b,vd(c))
using vc=vector<char>;
#define vvc(a, b, c) vec<vc> a(b,vc(c))
using vp = vector<P>;
#define vvp(a, b, c) vec<vp> a(b,vp(c))
using vt = vector<T>;
#define vvt(a, b, c) vec<vt> a(b,vt(c))
#define v3i(a, b, c, d) vector<vector<vi>> a(b, vector<vi>(c, vi(d)))
#define v3d(a, b, c, d) vector<vector<vd>> a(b, vector<vd>(c, vd(d)))
#define v3m(a, b, c, d) vector<vector<vm>> a(b, vector<vm>(c, vm(d)))

#define _vvi vector<vi>
#define _vvb vector<vb>
#define _vvs vector<vs>
#define _vvd vector<vd>
#define _vvc vector<vc>
#define _vvp vector<vp>

#define PQ priority_queue<ll, vector<ll>, greater<ll> >
#define tos to_string
using mapi = map<int, int>;
using mapd = map<dou, int>;
using mapc = map<char, int>;
using maps = map<str, int>;
using seti = set<int>;
using setd = set<dou>;
using setc = set<char>;
using sets = set<str>;
using qui = queue<int>;
#define bset bitset
#define uset unordered_set
#define mset multiset
#define umap unordered_map
#define umapi unordered_map<int,int>
#define mmap multimap

//マクロ 繰り返し
#define _overloadrep(_1, _2, _3, _4, name, ...) name
# define _rep(i, n) for(int i = 0,_lim=n; i < _lim ; i++)
#define repi(i, m, n) for(int i = m,_lim=n; i < _lim ; i++)
#define repadd(i, m, n, ad) for(int i = m,_lim=n; i < _lim ; i+= ad)
#define rep(...) _overloadrep(__VA_ARGS__,repadd,repi,_rep,)(__VA_ARGS__)
#define _rer(i, n) for(int i = n; i >= 0 ; i--)
#define reri(i, m, n) for(int i = m,_lim=n; i >= _lim ; i--)
#define rerdec(i, m, n, dec) for(int i = m,_lim=n; i >= _lim ; i-=dec)
#define rer(...) _overloadrep(__VA_ARGS__,rerdec,reri,_rer,)(__VA_ARGS__)
#define fora(a, b) for(auto&& a : b)
//#define forg(gi, ve) if (ve.size())for (int gi = 0, f = ve[gi].from, t = ve[gi].to, c = ve[gi].cost; gi < ve.size(); gi++,f = ve[gi].from, t = ve[gi].to, c = ve[gi].cost)
//                                                                           ve[gi]が参照外を指すのを防ぐ
#define forg(gi, ve) for (int gi = 0, f, t, c; gi < ve.size() && (f = ve[gi].from, t = ve[gi].to, c = ve[gi].cost, true); gi++)
#define fort(gi, ve) for (int gi = 0, f, t, c;((ve[gi].to==p?gi++:1),gi < ve.size()) && (f = ve[gi].from, t = ve[gi].to, c = ve[gi].cost, true);gi++ )

//マクロ 定数
#define k3 1010
#define k4 10101
#define k5 101010
#define k6 1010101
#define k7 10101010
const int inf = (int) 1e9 + 100;
const ll linf = (ll) 1e18 + 100;
const double eps = 1e-9;
const double PI = 3.1415926535897932384626433832795029L;
const int y4[] = {-1, 1, 0, 0};
const int x4[] = {0, 0, -1, 1};
const int y8[] = {0, 1, 0, -1, -1, 1, 1, -1};
const int x8[] = {1, 0, -1, 0, 1, -1, 1, -1};

//マクロ省略形 関数等
#define arsz(a) (sizeof(a)/sizeof(a[0]))
#define sz(a) ((int)(a).size())
#define rs(a) (a.resize())
#define mp make_pair
#define pb push_back
#define pf push_front
#define eb emplace_back
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()

//@拡張系 こう出来るべきというもの

//埋め込み 存在を意識せずに機能を増やされているもの
// 境界チェック付きvector
namespace std_vector_bounds_checking {
    using namespace std;
    template<class T, class A = std::allocator<T>> struct vector : std::vector<T, A> {
        using std::vector<T, A>::vector;
        typename std::vector<T>::reference operator[](typename std::vector<T>::size_type n) {
            return this->at(n);
        }
    };
}
namespace std {
    template<> class hash<std::pair<signed, signed>> {
    public:
        size_t operator()(const std::pair<signed, signed> &x) const {
            return hash<ll>()(((ll) x.first << 32) + x.second);
        }
    };
    template<> class hash<std::pair<ll, ll>> {
    public:
        size_t operator()(const std::pair<ll, ll> &x) const {
            return hash<ll>()(((ll) x.first << 32) + x.second);
        }
    };
}
istream &operator>>(istream &iss, P &a) {
    iss >> a.first >> a.second;
    return iss;
}
template<typename T> istream &operator>>(istream &iss, vector<T> &vec) {
    for (T &x: vec) iss >> x;
    return iss;
}
template<typename T> ostream &operator<<(ostream &os, vector <T> &vec) {
    for (int i = 0; i < vec.size(); i++)os << vec[i] << (i + 1 == vec.size() ? "" : " ");
    return os;
}
template<typename T> ostream &operator<<(ostream &os, vector <vector<T>> &vec) {
    for (int i = 0; i < vec.size(); i++) {
        for (int j = 0; j < vec[0].size(); j++) {
            os << vec[i][j];
        }
        os << endl;
    }
    return os;
}
template<typename V, typename H> void resize(vector<V> &vec, const H head) {  //再帰の終端。 可変長templateの長さが 0 になるとこっちが呼ばれる。
    vec.resize(head);
}
template<typename V, typename H, typename ... T> void resize(vector<V> &vec, const H &head, const T ... tail) {
    vec.resize(head);
    for (auto &v: vec) resize(v, tail...);
}
template<class T> T pop(set<T> &set) {
    T res = *set.begin();
    set.erase(set.find(res));
    return res;
}
template<class T> T pop(mset<T> &set) {
    T res = *set.begin();
    set.erase(set.find(res));
    return res;
}
template<class T> T popBack(set<T> &set) {
    T res = *set.rbegin();
    set.erase(set.find(res));
    return res;
}
template<class T> T popBack(mset<T> &set) {
    T res = *set.rbegin();
    set.erase(set.find(res));
    return res;
}
inline void sort(string &a) { sort(a.begin(), a.end()); }
template<class T> inline void sort(vector<T> &a) { sort(a.begin(), a.end()); };
template<class T> inline void sort(vector<T> &a, int len) { sort(a.begin(), a.begin() + len); };
template<class T, class F> inline void sort(vector<T> &a, F f) { sort(a.begin(), a.end(), [&](T l, T r) { return f(l) < f(r); }); };
template<class T> inline void rsort(vector<T> &a) { sort(a.begin(), a.end(), greater<T>()); };
template<class T> inline void rsort(vector<T> &a, int len) { sort(a.begin(), a.begin() + len, greater<T>()); };
template<class U, class F> inline void rsort(vector<U> &a, F f) { sort(a.begin(), a.end(), [&](U l, U r) { return f(l) > f(r); }); };
template<class U> inline void sortp(vector<U> &a, vector<U> &b) {
    vp c;
    int n = sz(a);
    assert(n == sz(b));
    rep(i, n)c.eb(a[i], b[i]);
    sort(c);
    rep(i, n) {
        a[i] = c[i].first;
        b[i] = c[i].second;;
    }
};
template<class U, class F> inline void sortp(vector<U> &a, vector<U> &b, F f) {
    vp c;
    int n = sz(a);
    assert(n == sz(b));
    rep(i, n)c.eb(a[i], b[i]);
    sort(c, f);
    rep(i, n) {
        a[i] = c[i].first;
        b[i] = c[i].second;
    }
};
template<class U, class F> inline void rsortp(vector<U> &a, vector<U> &b) {
    vp c;
    int n = sz(a);
    assert(n == sz(b));
    rep(i, n)c.eb(a[i], b[i]);
    rsort(c);
    rep(i, n) {
        a[i] = c[i].first;
        b[i] = c[i].second;
    }
};
template<class U, class F> inline void rsortp(vector<U> &a, vector<U> &b, F f) {
    vp c;
    int n = sz(a);
    assert(n == sz(b));
    rep(i, n)c.eb(a[i], b[i]);
    rsort(c, f);
    rep(i, n) {
        a[i] = c[i].first;
        b[i] = c[i].second;
    }
};
template<class U> inline void sortt(vector<U> &a, vector<U> &b, vector<U> &c) {
    vt r;
    int n = sz(a);
    assert(n == sz(b));
    assert(n == sz(c));
    rep(i, n)r.eb(a[i], b[i], c[i]);
    sort(r);
    rep(i, n) {
        a[i] = r[i].f;
        b[i] = r[i].s;
        c[i] = r[i].t;
    }
};
template<class U, class F> inline void sortt(vector<U> &a, vector<U> &b, vector<U> &c, F f) {
    vt r;
    int n = sz(a);
    assert(n == sz(b));
    assert(n == sz(c));
    rep(i, n)r.eb(a[i], b[i], c[i]);
    sort(r, f);
    rep(i, n) {
        a[i] = r[i].f;
        b[i] = r[i].s;
        c[i] = r[i].t;
    }
};
template<class U, class F> inline void rsortt(vector<U> &a, vector<U> &b, vector<U> &c, F f) {
    vt r;
    int n = sz(a);
    assert(n == sz(b));
    assert(n == sz(c));
    rep(i, n)r.eb(a[i], b[i], c[i]);
    rsort(r, f);
    rep(i, n) {
        a[i] = r[i].f;
        b[i] = r[i].s;
        c[i] = r[i].t;
    }
};
template<class T> inline void sort2(vector<vector<T>> &a) { for (int i = 0, n = a.size(); i < n; i++)sort(a[i]); }
template<class T> inline void rsort2(vector<vector<T>> &a) { for (int i = 0, n = a.size(); i < n; i++)rsort(a[i]); }
template<typename A, size_t N, typename T> void fill(A (&a)[N], const T &v) { rep(i, N)a[i] = v; }
template<typename A, size_t N, size_t O, typename T> void fill(A (&a)[N][O], const T &v) { rep(i, N)rep(j, O)a[i][j] = v; }
template<typename A, size_t N, size_t O, size_t P, typename T> void fill(A (&a)[N][O][P], const T &v) { rep(i, N)rep(j, O)rep(k, P)a[i][j][k] = v; }
template<typename A, size_t N, size_t O, size_t P, size_t Q, typename T> void fill(A (&a)[N][O][P][Q], const T &v) { rep(i, N)rep(j, O)rep(k, P)rep(l, Q)a[i][j][k][l] = v; }
template<typename A, size_t N, size_t O, size_t P, size_t Q, size_t R, typename T> void fill(A (&a)[N][O][P][Q][R], const T &v) { rep(i, N)rep(j, O)rep(k, P)rep(l, Q)rep(m, R)a[i][j][k][l][m] = v; }
template<typename A, size_t N, size_t O, size_t P, size_t Q, size_t R, size_t S, typename T> void fill(A (&a)[N][O][P][Q][R][S], const T &v) { rep(i, N)rep(j, O)rep(k, P)rep(l, Q)rep(m, R)rep(n, S)a[i][j][k][l][m][n] = v; }

template<typename V, typename T>
void fill(V &xx, const T vall) {
    xx = vall;
}
template<typename V, typename T>
void fill(vector<V> &vecc, const T vall) {
    for (auto &&vx: vecc) fill(vx, vall);
}

//@汎用便利関数 入力
template<typename T = int> T in() {
    T x;
    cin >> x;
    return (x);
}
string sin() { return in<string>(); }
double din() { return in<double>(); }
ll lin() { return in<ll>(); }
#define na(a, n) a.resize(n); rep(i,n) cin >> a[i];
#define nao(a, n) a.resize(n+1); rep(i,n) cin >> a[i+1];
#define nad(a, n) a.resize(n); rep(i,n) cin >> a[i], a[i]--;
#define na2(a, b, n) a.resize(n),b.resize(n);rep(i, n)cin >> a[i] >> b[i];
#define na2d(a, b, n) a.resize(n),b.resize(n);rep(i, n)cin >> a[i] >> b[i],a[i]--,b[i]--;
#define na3(a, b, c, n) a.resize(n),b.resize(n),c.resize(n);   rep(i, n)cin >> a[i] >> b[i] >> c[i];
#define na3d(a, b, c, n) a.resize(n),b.resize(n),c.resize(n);   rep(i, n)cin >> a[i] >> b[i] >> c[i],a[i]--,b[i]--,c[i]--;
#define nt(a, h, w) resize(a,h,w);rep(hi,h)rep(wi,w) cin >> a[hi][wi];
#define ntd(a, h, w) rs(a,h,w);rep(hi,h)rep(wi,w) cin >> a[hi][wi], a[hi][wi]--;
#define ntp(a, h, w) fill(a,'#');rep(hi,1,h+1)rep(wi,1,w+1) cin >> a[hi][wi];

//汎用便利関数 出力
template<class T> void out(T x) { typeid(x) == typeid(double) ? cout << fixed << setprecision(10) << x << endl : cout << x << endl; }
//デバッグ
#define sp << " " <<

#define debugName(VariableName) # VariableName

#define _deb1(x) cout <<  debugName(x)<<" = "<<x << endl
#define _deb2(x, y) cout <<  debugName(x)<<" = "<<x<<", "<< debugName(y)<<" = "<<y<< endl
#define _deb3(x, y, z) cout <<  debugName(x)<<" = "<<x  << ", " <<  debugName(y)<<" = "<<y <<", " debugName(z)<<" = "<<z <<endl
#define _deb4(x, y, z, a) cout <<  debugName(x)<<" = "<<x <<", " <<   debugName(y)<<" = "<<y <<", " <<  debugName(z)<<" = "<<z <<", " <<  debugName(a)<<" = "<<a<<endl
#define _deb5(x, y, z, a, b) cout <<  debugName(x)<<" = "<<x <<", " <<   debugName(y)<<" = "<<y <<", " <<  debugName(z)<<" = "<<z <<", " <<  debugName(a)<<" = "<<a<<", " <<  debugName(b)<<" = "<<b<<endl


#define _overloadebug(_1, _2, _3, _4, _5, name, ...) name
#define debug(...) _overloadebug(__VA_ARGS__,_deb5,_deb4,_deb3,_deb2,_deb1)(__VA_ARGS__)
#define deb(...) _overloadebug(__VA_ARGS__,_deb5,_deb4,_deb3,_deb2,_deb1)(__VA_ARGS__)


#define debugline(x) cerr << x << " " << "(L:" << __LINE__ << ")" << '\n'

//よく使うクラス、構造体
class UnionFind {
public:
    vi par, rank, sizes;
    int n, trees;
    UnionFind(int n) : n(n), trees(n) {
        par.resize(n), rank.resize(n), sizes.resize(n);
        rep(i, n)par[i] = i, sizes[i] = 1;
    }
    int root(int x) {
        if (par[x] == x)return x;
        else return par[x] = root(par[x]);
    }
    int find(int x) { return root(x); }
    void unite(int x, int y) {
        x = root(x);
        y = root(y);
        if (x == y)return;
        if (rank[x] < rank[y])swap(x, y);
        trees--;
        par[y] = x;
        sizes[x] += sizes[y];
        if (rank[x] == rank[y])rank[x]++;
    }
    bool same(int x, int y) { return root(x) == root(y); }
    int size(int x) { return sizes[root(x)]; }
    //順不同 umapなので
    vec<vi> sets() {
        vec<vi> res(trees);
        umap<int, vi> map;
        rep(i, n) map[root(i)].push_back(i);
        int i = 0;
        for (auto &&p:map) {
            int r = p.F;
            res[i].push_back(r);
            for (auto &&v:p.S) {
                if (r == v)continue;
                res[i].push_back(v);
            }
            i++;
        }
        return res;
    }
};

//MOD関連
ll MOD = (int) 1e9 + 7;
class mint {
public:
    int x;
    mint() : x(0) {}
    mint(signed y) : x(y >= 0 ? y % MOD : MOD - (-y) % MOD) {}
    mint(int y) : x(y >= 0 ? y % MOD : MOD - (-y) % MOD) {}
    static int _mpow(int v, ll a) {
        ll x = v, n = a, res = 1;
        while (n) {
            if (n & 1)res = (res * x) % MOD;
            x = (x * x) % MOD;
            n >>= 1;
        }
        return res;
    }

    // Arithmetic Oprators
    mint &operator+=(mint that) {
        if ((x += that.x) >= MOD) x -= MOD;
        return *this;
    }
    mint &operator-=(mint that) {
        if ((x += MOD - that.x) >= MOD) x -= MOD;
        return *this;
    }
    mint &operator*=(mint that) {
        x = 1LL * x * that.x % MOD;
        return *this;
    }
    mint &operator/=(const mint &that);
    mint &operator^=(const mint &that) {
        this->x = _mpow(x, that.x);
        return *this;
    }
    mint &operator%=(mint that) {
        x %= that.x;
        return *this;
    }

    mint &operator+=(const int that) { return *this += mint(that); }
    mint &operator-=(const int that) { return *this -= mint(that); }
    mint &operator*=(const int that) { return *this *= mint(that); }
    mint &operator/=(const int that);
    mint &operator^=(const int that) {
        this->x = _mpow(x, that);
        return *this;
    }
    mint &operator%=(const int that) { return *this %= mint(that); }

    mint &operator+=(const signed that) { return *this += mint(that); }
    mint &operator-=(const signed that) { return *this -= mint(that); }
    mint &operator*=(const signed that) { return *this *= mint(that); }
    mint &operator/=(const signed that);
    mint &operator^=(const signed that) {
        this->x = _mpow(x, that);
        return *this;
    }
    mint &operator%=(const signed that) { return *this %= mint(that); }

    // Comparators
    bool operator<(mint that) { return x < that.x; }
    bool operator>(mint that) { return x > that.x; }
    bool operator<=(mint that) { return x <= that.x; }
    bool operator>=(mint that) { return x >= that.x; }
    bool operator!=(mint that) { return x != that.x; }
    bool operator==(mint that) { return x == that.x; }
    bool operator!=(int that) { return x != that; }
    bool operator==(int that) { return x == that; }
    bool operator!=(signed that) { return x != that; }
    bool operator==(signed that) { return x == that; }

    // Utilities
    unsigned getval() const { return x; }
    operator int() { return x; }
    mint operator+(mint that) const { return mint(*this) += that; }
    mint operator-(mint that) const { return mint(*this) -= that; }
    mint operator*(mint that) const { return mint(*this) *= that; }
    mint operator%(mint that) const { return mint(*this) %= that; }
    mint operator+(const int that) const { return mint(*this) += that; }
    mint operator-(const int that) const { return mint(*this) -= that; }
    mint operator*(const int that) const { return mint(*this) *= that; }
    mint operator%(const int that) const { return mint(*this) %= that; }
    mint operator=(const int that) { return *this = mint(that); }
    mint operator+(const signed that) const { return mint(*this) += that; }
    mint operator-(const signed that) const { return mint(*this) -= that; }
    mint operator*(const signed that) const { return mint(*this) *= that; }
    mint operator%(const signed that) const { return mint(*this) %= that; }
    mint operator=(const signed that) { return *this = mint(that); }
    mint operator++() {
        x++;
        return *this;
    }
    mint operator++(signed) {
        auto ret = *this;
        x++;
        return ret;
    }
    friend void operator+=(ll &a, const mint &b) { a = mint(a % MOD + b.x); }
    friend void operator-=(ll &a, const mint &b) { a = mint(a % MOD - b.x); }
    friend void operator*=(ll &a, const mint &b) { a = mint(a % MOD * b.x); }
    friend void operator/=(ll &a, const mint &b);
    friend mint operator+(const ll a, const mint &b) { return mint(a % MOD + b.x); }
    friend mint operator-(const ll a, const mint &b) { return mint(a % MOD - b.x); }
    friend mint operator*(const ll a, const mint &b) { return mint(a % MOD * b.x); }
    friend mint operator^(const ll a, const mint &b) { return _mpow(a, b.x); }
};
mint itom(int v) {
    mint res;
    res.x = v;
    return res;
}
const int setModMax = 510000;
vector<mint> fac, finv, inv;
void setMod(int m = MOD) {
    fac.resize(setModMax);
    finv.resize(setModMax);
    inv.resize(setModMax);
    MOD = m;
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for (int i = 2; i < setModMax; i++) {
        fac[i] = fac[i - 1].x * i % MOD;
        inv[i] = MOD - inv[MOD % i].x * (MOD / i) % MOD;
        finv[i] = finv[i - 1].x * inv[i].x % MOD;
    }
}
mint mpow(int v, ll a) {
    return mint::_mpow(v, a);
}
mint com(ll n, ll r) {
    if (n < r || n < 0 || r < 0)return 0;
    if (fac.size() == 0)setMod();
    return fac[n] * finv[r] * finv[n - r];
}
mint ncr(ll n, ll r) { return com(n, r); }
mint nhr(ll n, ll r) { return com(n + r - 1, r); }

//拡張ユークリッドの互除法
mint minv(ll a) {
    if (fac[0] == 0)setMod();
    if (a < setModMax) return inv[a];
    a %= MOD;
    ll b = MOD, x = 1, y = 0;
    while (b) {
        ll t = a / b;
        a -= t * b;
        swap(a, b);
        x -= t * y;
        swap(x, y);
    }
    return x;
}
mint &mint::operator/=(const mint &that) { return *this *= minv(that.x); }
mint &mint::operator/=(const ll a) { return *this *= minv(a); }
mint &mint::operator/=(const signed a) { return *this *= minv(a); }
void operator/=(ll &a, const mint &b) { a = (a * minv(b.x)).x; }
using vm=vector<mint>;
#define vvm(a, b, c) vec<vm> a(b,vm(c))
using PM = pair<mint, mint>;
vb isPrime;
vi primes;

void setPrime() {
    isPrime.resize(4010101);
    fill(isPrime, true);
    int len = sizeof(isPrime) / sizeof(isPrime[0]);
    isPrime[0] = isPrime[1] = false;
    for (int i = 2; i <= sqrt(len) + 5; ++i) {
        if (!isPrime[i])continue;
        for (int j = 2; i * j < len; ++j) {
            isPrime[i * j] = false;
        }
    }
    rep(i, len)if (isPrime[i])primes.pb(i);
}
//幾何 Pをcomplexとして扱う
bool eq(double a, double b) { return fabs(a - b) < eps; }

using C =complex<double>;

C rot(C &a, dou th) {
    return a * C(cos(th), sin(th));
}

dou inpro(C &a, C &b) {
    return real(a * conj(b));
}

//90度回転させて内積が0なら平行
bool line(C a, C b, C c) {
    C ab = b - a;
    C ac = c - a;
    //複素数の掛け算は回転
    ab *= C(0, 1);
    return eq(inpro(ab, ac), 0);
}
bool line(P a, P b, P c) {
    return line(C(a.F, a.S), C(b.F, b.S), C(c.F, c.S));
}

bool line(int xa, int ya, int xb, int yb, int xc, int yc) {
    C a = C(xa, ya);
    C b = C(xb, yb);
    C c = C(xc, yc);
    return line(a, b, c);
}
//便利関数

//テスト用
char ranc() {
    return (char) ('a' + rand() % 26);
}
int rand(int min, int max) {
    assert(min <= max);
    if (min >= 0 && max >= 0) {
        return rand() % (max + 1 - min) + min;
    } else if (max < 0) {
        return -rand(-max, -min);
    } else {
        //+
        if (rand() % 2) {
            return rand(0, max);
            //-
        } else {
            return -rand(0, -min);
        }
    }
}
vi ranv(int n, int min, int max) {
    vi v(n);
    rep(i, n)v[i] = rand(min, max);
    return v;
}
//単調増加
vi ranvi(int n, int min, int max) {
    vi v(n);
    bool bad = 1;
    while (bad) {
        bad = 0;
        v.resize(n);
        rep(i, n) {
            if (i && min > max - v[i - 1]) {
                bad = 1;
                break;
            }
            if (i)v[i] = v[i - 1] + rand(min, max - v[i - 1]);
            else v[i] = rand(min, max);
        }
    }
    return v;
}
void ranvlr(int n, int min, int max, vi &l, vi &r) {
    l.resize(n);
    r.resize(n);
    rep(i, n) {
        l[i] = rand(min, max);
        r[i] = l[i] + rand(0, max - l[i]);
    }
}
int pow(int a) { return a * a; };
void iota(vector<int> &ve, int s, int n) {
    ve.resize(n);
    iota(all(ve), s);
}
vi iota(int s, int n) {
    vi ve;
    ve.resize(n);
    iota(all(ve), s);
    return ve;
}
void ole() {
#ifdef _DEBUG
    debugline("ole");
    exit(0);
#endif
    string a = "a";
    rep(i, 30)a += a;
    rep(i, 1 << 17)cout << a << endl;
    cout << "OLE 出力長制限超過" << endl;
    exit(0);
}
void tle() { while (inf)cout << inf << endl; }
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll gcd(vi b) {
    ll res = b[0];
    for (auto &&v :b)res = gcd(v, res);
    return res;
}
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
ll reverse(ll a) {
    ll res = 0;
    while (a) {
        res *= 10;
        res += a % 10;
        a /= 10;
    }
    return res;
}
template<class T> void reverse(vector<T> &a) {
    reverse(all(a));
}
ll ceil(ll a, ll b) {
    if (b == 0) {
        ole();
        return -1;
    } else return (a + b - 1) / b;
}
ll sqrt(ll a) {
    if (a < 0)ole();
    ll res = (ll) std::sqrt(a);
    while (res * res < a)res++;
    return res;
}
double log(double e, double x) { return log(x) / log(e); }
ll sig(ll t) { return (1 + t) * t / 2; }
ll sig(ll s, ll t) { return (s + t) * (t - s + 1) / 2; }

vi divisors(int v) {
    vi res;
    for (int i = 1; i <= sqrt(v); ++i) {
        if (v % i == 0) {
            res.pb(i);
            if (i != v / i)res.pb(v / i);
        }
    }
    return res;
}

vi factorization(int v) {
    int tv = v;
    vi res;
    if (isPrime.size() == 0)setPrime();
    for (auto &&p :primes) {
        if (v % p == 0)res.push_back(p);
        while (v % p == 0) {
            v /= p;
        }
        if (v == 1 || p * p > tv)break;
    }
    if (v > 1)res.pb(v);
    return res;
}

unordered_map<int, int> factorizationMap(int v) {
    int tv = v;
    unordered_map<int, int> res;
    if (isPrime.size() == 0)setPrime();
    for (auto &&p :primes) {
        while (v % p == 0) {
            res[p]++;
            v /= p;
        }
        if (v == 1 || p * p > tv)break;
    }
    if (v > 1)res[v]++;
    return res;
}
int get(int a, int keta) { return (a / (int) pow(10, keta)) % 10; }
int keta(int v) {
    int cou = 0;
    while (v) { cou++, v %= 10; }
    return cou;
}

template<class T> void imo(vector<T> &v) {
    int n = v.size();
    rep(i, n - 1)v[i + 1] += v[i];
}

//変換系
template<class T, class U> vector<T> keys(vector<pair<T, U>> a) {
    vector<T> res;
    for (auto &&k :a)res.pb(k.F);
    return res;
}
template<class T, class U> vector<U> keys(map<T, U> a) {
    vector<U> res;
    for (auto &&k :a)res.pb(k.F);
    return res;
}

template<class T, class U> vector<U> keys(umap<T, U> a) {
    vector<U> res;
    for (auto &&k :a)res.pb(k.F);
    return res;
}

template<class T, class U> vector<U> values(vector<pair<T, U>> a) {
    vector<U> res;
    for (auto &&k :a)res.pb(k.S);
    return res;
}

template<class T, class U> vector<T> values(map<T, U> a) {
    vector<T> res;
    for (auto &&k :a)res.pb(k.S);
    return res;
}

template<class T, class U> vector<T> values(umap<T, U> a) {
    vector<T> res;
    for (auto &&k :a)res.pb(k.S);
    return res;
}

vi list(int a) {
    vi res;
    while (a) {
        res.insert(res.begin(), a % 10);
        a /= 10;
    }
    return res;
}

template<class T, class U> bool chmax(T &a, const U &b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template<class T, class U> bool chmin(T &a, const U &b) {
    if (b < a) {
        a = b;
        return true;
    }
    return false;
}

template<class T> T min(T a, signed b) {
    return a < b ? a : b;
}

template<class T> T max(T a, signed b) {
    return a < b ? b : a;
}

template<class T> T min(T a, T b, T c) {
    return a >= b ? b >= c ? c : b : a >= c ? c : a;
}
template<class T> T max(T a, T b, T c) {
    return a <= b ? b <= c ? c : b : a <= c ? c : a;
}

template<class T> T min(vector<T> a) {
    return *min_element(all(a));
}
template<class T> T min(vector<T> a, int n) {
    return *min_element(a.begin(), a.begin() + min(n, sz(a)));
}
template<class T> T min(vector<T> a, int s, int n) {
    return *min_element(a.begin() + s, a.begin() + min(n, sz(a)));
}
template<class T> T max(vector<T> a) {
    return *max_element(all(a));
}
template<class T> T max(vector<T> a, int n) {
    return *max_element(a.begin(), a.begin() + min(n, sz(a)));
}
template<class T> T max(vector<T> a, int s, int n) {
    return *max_element(a.begin() + s, a.begin() + min(n, sz(a)));
}
template<typename A, size_t N> A max(A (&a)[N]) {
    A res = a[0];
    rep(i, N)res = max(res, a[i]);
    return res;
}
template<typename A, size_t N, size_t O> A max(A (&a)[N][O]) {
    A res = max(a[0]);
    rep(i, N)res = max(res, max(a[i]));
    return res;
}
template<typename A, size_t N, size_t O, size_t P> A max(A (&a)[N][O][P]) {
    A res = max(a[0]);
    rep(i, N)res = max(res, max(a[i]));
    return res;
}
template<typename A, size_t N, size_t O, size_t P, size_t Q> A max(A (&a)[N][O][P][Q], const T &v) {
    A res = max(a[0]);
    rep(i, N)res = max(res, max(a[i]));
    return res;
}
template<typename A, size_t N, size_t O, size_t P, size_t Q, size_t R> A max(A (&a)[N][O][P][Q][R]) {
    A res = max(a[0]);
    rep(i, N)res = max(res, max(a[i]));
    return res;
}
template<typename A, size_t N, size_t O, size_t P, size_t Q, size_t R, size_t S> A max(A (&a)[N][O][P][Q][R][S]) {
    A res = max(a[0]);
    rep(i, N)res = max(res, max(a[i]));
    return res;
}
template<typename A, size_t N> A min(A (&a)[N]) {
    A res = a[0];
    rep(i, N)res = min(res, a[i]);
    return res;
}
template<typename A, size_t N, size_t O> A min(A (&a)[N][O]) {
    A res = min(a[0]);
    rep(i, N)res = min(res, max(a[i]));
    return res;
}
template<typename A, size_t N, size_t O, size_t P> A min(A (&a)[N][O][P]) {
    A res = min(a[0]);
    rep(i, N)res = min(res, min(a[i]));
    return res;
}
template<typename A, size_t N, size_t O, size_t P, size_t Q> A min(A (&a)[N][O][P][Q], const T &v) {
    A res = min(a[0]);
    rep(i, N)res = min(res, min(a[i]));
    return res;
}
template<typename A, size_t N, size_t O, size_t P, size_t Q, size_t R> A min(A (&a)[N][O][P][Q][R]) {
    A res = min(a[0]);
    rep(i, N)res = min(res, min(a[i]));
    return res;
}
template<typename A, size_t N, size_t O, size_t P, size_t Q, size_t R, size_t S> A min(A (&a)[N][O][P][Q][R][S]) {
    A res = min(a[0]);
    rep(i, N)res = min(res, min(a[i]));
    return res;
}


template<class T> T sum(vector<T> v, int len = -1) {
    if (len == -1)len = v.size();
    T res = 0;
    chmin(len, v.size());
    rep(i, len)res += v[i];
    return res;
}
template<class T> T sum(vector<vector<T>> &v, int h = -1, int w = -1) {
    if (h == -1)h = v.size();
    if (w == -1)w = v[0].size();
    T res = 0;
    chmin(h, v.size());
    chmin(w, v[0].size());
    rep(i, h)rep(j, w)res += v[i][j];
    return res;
}

P sump(vp &v, int len = -1) {
    if (len == -1)len = v.size();
    P res = {0, 0};
    chmin(len, v.size());
    rep(i, len) {
        res.F += v[i].F;
        res.S += v[i].S;
    }
    return res;
}

///要素が0の時、返り値は0か1か
template<class T> T mul(vector<T> &v, int len = -1) {
    if (len == -1)len = v.size();
    T res = 1;
    chmin(len, v.size());
    rep(i, len)res *= v[i];
    return res;
}
void clear(PQ &q) { while (q.size())q.pop(); }
template<class T> void clear(queue<T> &q) { while (q.size())q.pop(); }
template<class T> T *negarr(int size) {
    T *body = (T *) malloc((size * 2 + 1) * sizeof(T));
    return body + size;
}
template<class T> T *negarr2(int h, int w) {
    double **dummy1 = new double *[2 * h + 1];
    double *dummy2 = new double[(2 * h + 1) * (2 * w + 1)];
    dummy1[0] = dummy2 + w;
    for (int i = 1; i <= 2 * h + 1; i++) {
        dummy1[i] = dummy1[i - 1] + 2 * w + 1;
    }
    double **a = dummy1 + h;
}
template<class T> struct ruic {
    const vector<T> rui;
    ruic(vector<T> &ru) : rui(ru) {}
    T operator()(int l, int r) {
        assert(l <= r);
        return rui[r] - rui[l];
    }
    T operator[](int i) {
        return rui[i];
    }
};

template<class T> struct rruic {
    const T *rrui;
    rruic(T *ru) : rrui(ru) {}
    //n-1から-1へ
    T operator()(int l, int r) {
        assert(l >= r);
        return rrui[r] - rrui[l];
    }
    T operator[](int i) {
        return rrui[i];
    }
};
//template<class T> vector<T> ruiv(vector<T> &a)
template<class T> ruic<T> ruiv(vector<T> &a) {
    vector<T> res(a.size() + 1);
    rep(i, a.size())res[i + 1] = res[i] + a[i];
    return ruic<T>(res);
}

template<class T> vector<T> ruim(vector<T> &a) {
    vector<T> res(a.size() + 1, 1);
    rep(i, a.size())res[i + 1] = res[i] * a[i];
    return res;
}
//template<class T> T *rrui(vector<T> &a) {
//右から左にかけての半開区間 (-1 n-1]
template<class T> rruic<T> rrui(vector<T> &a) {
    int len = a.size();
    T *body = (T *) malloc((len + 1) * sizeof(T));
    T *res = body + 1;
    rer(i, len - 1)res[i - 1] = res[i] + a[i];
    return rruic<T>(res);
}
//掛け算
template<class T> T *rruim(vector<T> &a) {
    int len = a.size();
    T *body = (T *) malloc((len + 1) * sizeof(T));
    T *res = body + 1;
    res[len - 1] = 1;
    rer(i, len - 1)res[i - 1] = res[i] * a[i];
    return res;
}
template<class T> void plus(vector<T> &a, T v = 1) { for (auto &&u :a)u += v; }
template<class T> void minu(vector<T> &a, T v = 1) { for (auto &&u :a)u -= v; }
template<class T> void minus(vector<T> &a, T v = 1) { for (auto &&u :a)u -= v; }
inline bool inside(int y, int x, int H, int W) { return y >= 0 && x >= 0 && y < H && x < W; }
ll u(ll a) { return a < 0 ? 0 : a; }
template<class T> vector<T> u(const vector<T> &a) {
    vector<T> ret = a;
    fora(v, ret)v = u(v);
    return ret;
}
#define MIN(a) numeric_limits<a>::min()
#define MAX(a) numeric_limits<a>::max()
ll goldd(ll left, ll right, function<ll(ll)> calc) {
    double GRATIO = 1.6180339887498948482045868343656;
    ll lm = left + (ll) ((right - left) / (GRATIO + 1.0));
    ll rm = lm + (ll) ((right - lm) / (GRATIO + 1.0));
    ll fl = calc(lm);
    ll fr = calc(rm);
    while (right - left > 10) {
        if (fl < fr) {
            right = rm;
            rm = lm;
            fr = fl;
            lm = left + (ll) ((right - left) / (GRATIO + 1.0));
            fl = calc(lm);
        } else {
            left = lm;
            lm = rm;
            fl = fr;
            rm = lm + (ll) ((right - lm) / (GRATIO + 1.0));
            fr = calc(rm);
        }
    }
    ll minScore = MAX(ll);
    ll resIndex = left;
    for (ll i = left; i < right + 1; i++) {
        ll score = calc(i);
        if (minScore > score) {
            minScore = score;
            resIndex = i;
        }
    }
    return resIndex;
}
ll goldt(ll left, ll right, function<ll(ll)> calc) {
    double GRATIO = 1.6180339887498948482045868343656;
    ll lm = left + (ll) ((right - left) / (GRATIO + 1.0));
    ll rm = lm + (ll) ((right - lm) / (GRATIO + 1.0));
    ll fl = calc(lm);
    ll fr = calc(rm);
    while (right - left > 10) {
        if (fl > fr) {
            right = rm;
            rm = lm;
            fr = fl;
            lm = left + (ll) ((right - left) / (GRATIO + 1.0));
            fl = calc(lm);
        } else {
            left = lm;
            lm = rm;
            fl = fr;
            rm = lm + (ll) ((right - lm) / (GRATIO + 1.0));
            fr = calc(rm);
        }
    }
    if (left > right) {
        ll l = left;
        left = right;
        right = l;
    }
    ll maxScore = MIN(ll);
    ll resIndex = left;
    for (ll i = left; i < right + 1; i++) {
        ll score = calc(i);
        if (maxScore < score) {
            maxScore = score;
            resIndex = i;
        }
    }
    return resIndex;
}
template<class T> T min(vector<vector<T>> &a) {
    T res = MAX(T);
    rep(i, a.size())chmin(res, *min_element(all(a[i])));
    return res;
}
template<class T> T max(vector<vector<T>> &a) {
    T res = MIN(T);
    rep(i, a.size())chmax(res, *max_element(all(a[i])));
    return res;
}

bool bget(ll m, int keta) { return (m >> keta) & 1; }
int bget(ll m, int keta, int sinsuu) {
    m /= (ll) pow(sinsuu, keta);
    return m % sinsuu;
}
inline ll bit(int n) { return (1LL << (n)); }
inline ll bit(int n, int sinsuu) { return (ll) pow(sinsuu, n); }
int bcou(ll m) { return __builtin_popcount(m & 0xFFFFFFFF) + __builtin_popcount(m >> 32); }
//初期化は0を渡す
ll nextComb(ll &mask, int n, int r) {
    if (!mask)return mask = (1LL << r) - 1;
    ll x = mask & -mask; //最下位の1
    ll y = mask + x; //連続した下の1を繰り上がらせる
    ll res = ((mask & ~y) / x >> 1) | y;
    if (bget(res, n))return mask = 0;
    else return mask = res;
}

//n桁以下でビットがr個立っているもののvectorを返す
vl bitCombList(int n, int r) {
    vl res;
    int m = 0;
    while (nextComb(m, n, r)) {
        res.pb(m);
    }
    return res;
}
//大文字小文字を区別する
int altoiaZ(char c) {
    if ('A' <= c && c <= 'Z')return c - 'A';
    return c - 'a' + 26;
}
char itoalaZ(int i) {
    if (i < 26)return 'A' + i;
    return 'a' + i - 26;
}
//aもAも0を返す 基本小文字
int altoi(char c) {
    if ('A' <= c && c <= 'Z')return c - 'A';
    return c - 'a';
}
char itoal(int i) {
    return 'a' + i;
}
int ctoi(char c) { return c - '0'; }
char itoc(int i) { return i + '0'; }
int vtoi(vi &v) {
    int res = 0;
    if (sz(v) > 18)ole();
    rep(i, sz(v)) {
        res *= 10;
        res += v[i];
    }
    return res;
}
vi itov(int i) {
    vi res;
    while (i) {
        res.pb(i % 10);
        i /= 10;
    }
    reverse(res);
    return res;
}
vector<vector<int>> ctoi(vector<vector<char>> s, char c) {
    int n = sz(s), m = sz(s[0]);
    vector<vector<int>> res(n, vector<int>(m));
    rep(i, n)rep(j, m)res[i][j] = s[i][j] == c;
    return res;
}
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );

void compress(vi &a) {
    vi b;
    int len = a.size();
    for (int i = 0; i < len; ++i) {
        b.push_back(a[i]);
    }
    sort(b);
    UNIQUE(b);
    for (int i = 0; i < len; ++i) {
        a[i] = lower_bound(all(b), a[i]) - b.begin();
    }
}

void compress(int a[], int len) {
    vi b;
    for (int i = 0; i < len; ++i) {
        b.push_back(a[i]);
    }
    sort(b);
    UNIQUE(b);
    for (int i = 0; i < len; ++i) {
        a[i] = lower_bound(all(b), a[i]) - b.begin();
    }
}
//要素が見つからなかったときに困る
#define binarySearch(a, v) (binary_search(all(a),v))
#define lowerIndex(a, v) (lower_bound(all(a),v)-a.begin())
#define lowerBound(a, v) (*lower_bound(all(a),v))
#define upperIndex(a, v) (upper_bound(all(a),v)-a.begin())
#define upperBound(a, v) (*upper_bound(all(a),v))
#define ans(a) cout<<a<<endl;continue;
#define poll(a) q.front();q.pop()
#define dpoll(a) q.front();q.pop_front()
#define pollLast(a) q.back();q.pop_back()
#define pollBack(a) q.back();q.pop_back()
template<class T> inline void fin(T s) { cout << s << endl, exit(0); }

template<class T> struct edge {
    int from, to;
    T cost;
    int id;
    int type;
    edge(int f, int t, T c = 1, int id = -1, int ty = -1) : from(f), to(t), cost(c), id(id), type(ty) {}
    bool operator<(const edge &b) const { return cost < b.cost; }
    bool operator>(const edge &b) const { return cost > b.cost; }
};

template<typename T> class graph {
protected:
    vector<bool> _used;
public :
    vector<vector<edge<T>>> g;
    vector<edge<T>> edges;
    int n, root = -1;
    graph(int n) : n(n) { g.resize(n), _used.resize(n); }
    void clear() { g.clear(), edges.clear(); }
    void resize(int n) {
        this->n = n;
        g.resize(n);
        _used.resize(n);
    }
    int size() { return g.size(); }
    bool isleaf(int v) {
        assert(root != -1);
        return g[v].size() == 1 && g[v][0].from != root;
    }
    vector<edge<T> > &operator[](int i) { return g[i]; }
    virtual void add(int from, int to, T cost, int id, int ty) = 0;
    virtual bool used(edge<T> &e) = 0;
    virtual bool used(int id) = 0;
    virtual void del(edge<T> &e) = 0;
    virtual void del(int id) = 0;
};

template<class T=int> class undigraph : public graph<T> {
public:
    using graph<T>::g;
    using graph<T>::n;
    using graph<T>::edges;
    using graph<T>::_used;
    undigraph(int n) : graph<T>(n) {
    }
    void add(int f, int t, T cost = 1, int id = -1, int ty = -1) {
        if (!(0 <= f && f < n && 0 <= t && t < n))ole();
        if (id == -1)id = edges.size();
        g[f].emplace_back(f, t, cost, id, ty);
        g[t].emplace_back(t, f, cost, id + 1, ty);
        edges.emplace_back(f, t, cost, id, ty);
        edges.emplace_back(t, f, cost, id + 1, ty);
    }
    void add(edge<T> &e) {
        int f = e.from, t = e.to, ty = e.type;
        T cost = e.cost;
        add(f, t, cost, ty);
    }
    bool used(edge<T> &e) { return _used[e.id]; }
    bool used(int id) { return _used[id]; }
    void del(edge<T> &e) { _used[e.id] = _used[e.id ^ 1] = 1; }
    void del(int id) { _used[id] = _used[id ^ 1] = 1; }
};

template<typename T =ll> class digraph : public graph<T> {
public:
    using graph<T>::g;
    using graph<T>::n;
    using graph<T>::edges;
    using graph<T>::_used;

    digraph(int n) : graph<T>(n) {}
    void add(int f, int t, T cost = 1, int id = -1, int ty = -1) {
        if (!(0 <= f && f < n && 0 <= t && t < n))ole();
        if (id == -1)id = edges.size();
        g[f].emplace_back(f, t, cost, id, ty);
        edges.emplace_back(f, t, cost, id, ty);
    }
    bool used(edge<T> &e) { return _used[e.id]; }
    bool used(int id) { return _used[id]; }
    void del(edge<T> &e) { _used[e.id] = _used[e.id ^ 1] = 1; }
    void del(int id) { _used[id] = _used[id ^ 1] = 1; }
};

template<class T> bool nibu(const graph<T> &g) {
    if (g.edges.size() == 0)return true;
    UnionFind uf(g.n * 2);
    for (auto &&e :g.edges)uf.unite(e.from, e.to + g.n), uf.unite(e.from + g.n, e.to);
    rep(i, g.n)if (uf.same(i, i + g.n))return 0;
    return 1;
}
//二部グラフを色分けした際の頂点数を返す
template<class T> vp nibug(graph<T> &g) {
    vp cg;
    if (!nibu(g))ole();
    int _n = g.size();
    vb _was(_n);
    queue<P> q;
    rep(i, _n) {
        if (_was[i])continue;
        q.push(mp(i, 1));
        _was[i] = 1;
        int red = 0;
        int coun = 0;
        while (q.size()) {
            int now = q.front().F;
            int col = q.front().S;
            red += col;
            coun++;
            q.pop();
            forg(gi, g[now]) {
                if (_was[t])continue;
                q.push(mp(t, col ^ 1));
                _was[t] = 1;
            }
        }
        cg.push_back(mp(red, coun - red));
    }
    return cg;

}

template<class T> vector<T> dijkstra(const graph<T> &g, int s) {
    if (!(0 <= s && s < g.n))ole();
    T initValue = MAX(T);
    vector<T> dis(g.n, initValue);
    priority_queue<pair<T, int>, vector<pair<T, int>>, greater<pair<T, int>>> q;
    dis[s] = 0;
    q.emplace(0, s);
    while (q.size()) {
        T nowc = q.top().F;
        int i = q.top().S;
        q.pop();
        if (dis[i] != nowc)continue;
        for (auto &&e  : g.g[i]) {
            int to = e.to;
            T cost = nowc + e.cost;
            if (dis[to] > cost) {
                dis[to] = cost;
                q.emplace(dis[to], to);
            }
        }
    }
    //たどり着かないなら-1
    for (auto &&d :dis) if (d == initValue)d = -1;
    return dis;
}

//機能拡張
vp vtop(vi &a, vi &b) {
    vp res(sz(a));
    rep(i, sz(a))res[i] = mp(a[i], b[i]);
    return res;
}
void ptov(vp &p, vi &a, vi &b) {
    a.resize(sz(p));
    b.resize(sz(p));
    rep(i, sz(p))a[i] = p[i].F, b[i] = p[i].S;
}
template<typename _CharT, typename _Traits, typename _Alloc>
basic_string<_CharT, _Traits, _Alloc>
operator+(const basic_string<_CharT, _Traits, _Alloc> &__lhs, const int __rv) {
    basic_string<_CharT, _Traits, _Alloc> __str(__lhs);
    __str.append(to_string(__rv));
    return __str;
}
template<typename _CharT, typename _Traits, typename _Alloc>
void operator+=(basic_string<_CharT, _Traits, _Alloc> &__lhs, const int __rv) {
    __lhs += to_string(__rv);
}
template<typename _CharT, typename _Traits, typename _Alloc>
basic_string<_CharT, _Traits, _Alloc>
operator+(const basic_string<_CharT, _Traits, _Alloc> &__lhs, const signed __rv) {
    basic_string<_CharT, _Traits, _Alloc> __str(__lhs);
    __str.append(to_string(__rv));
    return __str;
}
template<typename _CharT, typename _Traits, typename _Alloc>
void operator+=(basic_string<_CharT, _Traits, _Alloc> &__lhs, const signed __rv) {
    __lhs += to_string(__rv);
}
template<class T, class U> void operator+=(queue<T> &a, U v) {
    a.push(v);
}
template<class T, class U>
priority_queue<T, vector<T>, greater<T> > &operator+=(priority_queue<T, vector<T>, greater<T> > &a, U v) {
    a.push(v);
    return a;
}
template<class T, class U> priority_queue<T> &operator+=(priority_queue<T> &a, U v) {
    a.push(v);
    return a;
}
template<class T, class U> set<T> &operator+=(set<T> &a, U v) {
    a.insert(v);
    return a;
}
template<class T, class U> set<T, greater<T>> &operator+=(set<T, greater<T>> &a, U v) {
    a.insert(v);
    return a;
}

template<class T, class U> vector<T> &operator+=(vector<T> &a, U v) {
    a.pb(v);
    return a;
}
template<class T> vector<T> &operator+=(vector<T> &a, vector <T> &b) {
    a.pb(b);
    return a;
}
template<class T, class U> vector<T> &operator+=(vector<T> &a, initializer_list<U> v) {
    for (auto &&va :v)a.pb(va);
    return a;
}
template<class T> vector<T> &operator-=(vector<T> &a, vector <T> &b) {
    if (sz(a) != sz(b))ole();
    rep(i, sz(a))a[i] -= b[i];
    return a;
}
template<class T> vector<T> &operator-(vector<T> &a, vector <T> &b) {
    if (sz(a) != sz(b))ole();
    vector<T> res;
    rep(i, sz(a))res[i] = a[i] - b[i];
    return res;
}


template<typename T> void remove(vector<T> &v, unsigned int i) { v.erase(v.begin() + i); }
template<typename T> void remove(vector<T> &v, unsigned int s, unsigned int e) {
    v.erase(v.begin() + s, v.begin() + e);
}
template<typename T> void removen(vector<T> &v, unsigned int s, unsigned int n) {
    v.erase(v.begin() + s, v.begin() + s + n);
}
template<typename T> void erase(vector<T> &v, unsigned int i) { v.erase(v.begin() + i); }
template<typename T> void erase(vector<T> &v, unsigned int s, unsigned int e) {
    v.erase(v.begin() + s, v.begin() + e);
}
template<typename T> void erasen(vector<T> &v, unsigned int s, unsigned int n) {
    v.erase(v.begin() + s, v.begin() + s + n);
}
template<typename T> void insert(vector<T> &v, unsigned int i, T t) { v.insert(v.begin() + i, t); }
template<typename T> void insert(vector<T> &v, unsigned int i, vector<T> list) {
    for (auto &&va :list)v.insert(v.begin() + i++, va);
}
template<typename T, typename U> void insert(vector<T> &v, initializer_list<U> list) {
    for (auto &&va :list)v.pb(va);
}
template<typename T, typename U> void insert(vector<T> &v, unsigned int i, initializer_list<U> list) {
    for (auto &&va :list)v.insert(v.begin() + i++, va);
}
template<typename T> void insert(set<T> &v, vector<T> list) {
    for (auto &&va :list)v.insert(va);
}
template<typename T> void insert(set<T> &v, initializer_list<T> list) {
    for (auto &&va :list)v.insert(va);
}


ll ma = numeric_limits<ll>::min();
ll mi = numeric_limits<ll>::max();
//閉路がなければtrue
bool topo(vi &res, digraph<int> &g) {
    int n = g.g.size();
    vi nyu(n);
    rep(i, n)for (auto &&e :g[i])nyu[e.to]++;
    queue<int> st;
    rep(i, n)if (nyu[i] == 0)st.push(i);
    while (st.size()) {
        int v = st.front();
        st.pop();
        res.pb(v);
        fora(e, g[v]) if (--nyu[e.to] == 0)st.push(e.to);
    }
    return res.size() == n;
}
//辞書順最小トポロジカルソート
bool topos(vi &res, digraph<int> &g) {
    int n = g.g.size();
    vi nyu(n);
    rep(i, n)for (auto &&e :g[i])nyu[e.to]++;
    //小さい順
    priority_queue<int, vector<int>, greater<int> > q;
    rep(i, n)if (nyu[i] == 0)q.push(i);
    while (q.size()) {
        int i = q.top();
        q.pop();
        res.pb(i);
        fora(e, g[i])if (--nyu[e.to] == 0)q.push(e.to);
    }
    return res.size() == n;
}
vector<string> split(const string a, const char deli) {
    string b = a + deli;
    int l = 0, r = 0, n = b.size();
    vector<string> res;
    rep(i, n) {
        if (b[i] == deli) {
            r = i;
            if (l < r)res.push_back(b.substr(l, r - l));
            l = i + 1;
        }
    }
    return res;
}
vector<string> split(const string a, const string deli) {
    string b = a + deli;
    int l = 0, r = 0, n = b.size(), dn = deli.size();
    vector<string> res;
    rep(i, n) {
        if (i + dn <= n && b.substr(i, i + dn) == deli) {
            r = i;
            if (l < r)res.push_back(b.substr(l, r - l));
            i += dn - 1;
            l = i + 1;
        }
    }
    return res;
}
void yn(bool a) {
    if (a)cout << "yes" << endl;
    else cout << "no" << endl;
}
void Yn(bool a) {
    if (a)cout << "Yes" << endl;
    else cout << "No" << endl;
}
void YN(bool a) {
    if (a)cout << "YES" << endl;
    else cout << "NO" << endl;
}
void fyn(bool a) {
    if (a)cout << "yes" << endl;
    else cout << "no" << endl;
    exit(0);
}
void fYn(bool a) {
    if (a)cout << "Yes" << endl;
    else cout << "No" << endl;
    exit(0);
}
void fYN(bool a) {
    if (a)cout << "YES" << endl;
    else cout << "NO" << endl;
    exit(0);
}
void Possible(bool a) {
    if (a)cout << "Possible" << endl;
    else cout << "Impossible" << endl;
    exit(0);
}


int n, m, k, d, H, W, x, y, z, q;
int cou;
vi a, b, c;
vvi (s, 0, 0);
vvc (ba, 0, 0);
vp p;
undigraph<> g(2 * k5);
void solve() {
    cin >> n;
    na(a, n);
    rep(i, n - 1) {
        int f, t;
        cin >> f >> t;
        --f, --t;
        g.add(f, t);
    }
    if (n == 2) {
        fYN(a[0] == a[1] && a[0] == 1);
    } else {
        //親との辺のコストを返す
        function<int(int, int)> ds = [&](int i, int p){
            if (sz(g[i]) == 1) {
                return a[i];
            } else {
                vi cost;
                fort(gi, g[i]) {
                    int co = ds(t, i);
                    if (co > a[i] || co < 0)return -1ll;
                    cost += co;
                }
                int co = a[i] * 2 - sum(cost);
                if (co > a[i] || co < 0)return -1ll;
                return co;
            }
        };
        rep(i, n) {
            if (sz(g[i]) > 1) {
                fYN(ds(i, -1) == 0);
            }
        }
    }

}
int my(int n, vi a) {
    return 0;
}
int sister(int n, vi a) {
    return 0;
}

signed main() {
    solve();

#define _arg n,a
    //cin>>n;
    //na(a,n);
    //my(_arg);
    //cout << my(_arg) << endl;
#ifdef _DEBUG
    bool bad = 0;
    for (int i = 0, ok = 1; i < k5 && ok; i++) {
        int n = rand(1, 3);
        vi a = ranv(m, 1, 10);
        int myres = my(_arg);
        int res = sister(_arg);
        ok = myres == res;
        if (!ok) {
            cout << n << endl;
            cout << a << endl;
            cout << "正解 : " << res << endl;
            cout << "出力 : " << myres << endl;
            bad = 1;
            break;
        }
    }
//    if (!bad)cout << "お兄ちゃんすごい！天才！！" << endl;
#endif
    return 0;
};