/**
 * 
 */

// #include {{{
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <forward_list>
#include <functional>
#include <iomanip>
#include <iostream>
#include <fstream>
#include <sstream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <regex>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#ifdef DEBUG
#include <fmt/format.h>
#include <fmt/ostream.h>
#endif

using namespace std;
// }}}

// type {{{
using  i8 =   int8_t;
using  u8 =  uint8_t;
using i16 =  int16_t;
using u16 = uint16_t;
using i32 =  int32_t;
using u32 = uint32_t;
using i64 =  int64_t;
using u64 = uint64_t;

template<typename T>
using max_heap = priority_queue<T, vector<T>, less<T>>;
template<typename T>
using min_heap = priority_queue<T, vector<T>, greater<T>>;
// }}}

// hide {{{
#ifdef __clang__
#pragma clang diagnostic push
#pragma clang diagnostic ignored "-Wunused-const-variable"
#endif
// }}}

// 適宜調整
//#define int i64
//#define double long double

constexpr bool AUTOFLUSH = false;

constexpr bool STDIO_ENABLE = false;

constexpr int IOS_PREC = 12;

constexpr int INF_I32 =             1'010'000'000;
constexpr i64 INF_I64 = 1'010'000'000'000'000'000LL;

constexpr auto   INF = INF_I64;
constexpr double EPS = 1e-12;

constexpr i64 MOD = 1'000'000'007;

// hide {{{
#ifdef __clang__
#pragma clang diagnostic pop
#endif
// }}}

// util {{{
constexpr i32 I32_MAX = numeric_limits<i32>::max();
constexpr i32 I32_MIN = numeric_limits<i32>::min();

constexpr i64 I64_MAX = numeric_limits<i64>::max();
constexpr i64 I64_MIN = numeric_limits<i64>::min();

template<typename T, size_t N, size_t... NS>
struct ArrayStruct {
    using type = array<typename ArrayStruct<T,NS...>::type,N>;
};

template<typename T, size_t N>
struct ArrayStruct<T,N> {
    using type = array<T,N>;
};

template<typename T, size_t N, size_t... NS>
using Array = typename ArrayStruct<T,N,NS...>::type;

template<typename T>
int GETBIT(T x, int i) {
    return (x>>i) & 1;
}

template<typename T>
void SETBIT(T& x, int i) {
    x |= (T(1)<<i);
}

template<typename T>
void CLEARBIT(T& x, int i) {
    x &= ~(T(1)<<i);
}

template<typename T>
constexpr T ABS(T x) {
    static_assert(is_signed<T>::value, "ABS(): argument must be signed");
    return x < 0 ? -x : x;
}

template<typename T>
constexpr T abs_diff(T x, T y) {
    return x < y ? y-x : x-y;
}

constexpr i64 MID(i64 x, i64 y) {
    i64 lo = min(x, y);
    i64 hi = max(x, y);

    return (lo < 0 && hi >= 0) ? (lo+hi)/2 : lo + (hi-lo)/2;
}

// lo:OK, hi:NG
template<typename Pred>
i64 bin_search(i64 lo, i64 hi, Pred pred) {
    assert(lo < hi);

    while(lo+1 < hi) {
        i64 mid = MID(lo, hi);
        if(pred(mid))
            lo = mid;
        else
            hi = mid;
    }
    return lo;
}

template<typename Pred>
double bin_search_real(double lo, double hi, Pred pred, int iter=100) {
    assert(lo < hi);

    for(int i = 0; i < iter; ++i) {
        double mid = (lo+hi) / 2.0;
        if(pred(mid))
            lo = mid;
        else
            hi = mid;
    }
    return lo;
}

template<typename T>
constexpr bool is_odd(T x) {
    return x % 2 != 0;
}

template<typename T>
constexpr bool is_even(T x) {
    return x % 2 == 0;
}

template<typename T>
constexpr bool parity_same(T x, T y) {
    return (is_odd(x) && is_odd(y)) || (is_even(x) && is_even(y));
}

template<typename T>
constexpr int cmp(T x, T y) {
    return (y < x) - (x < y);
}

template<typename T>
constexpr int sgn(T x) {
    return cmp(x, T(0));
}

template<typename T>
constexpr T ipow(T a, T b) {
    assert(b >= 0);
    T res(1);
    for(T i = 0; i < b; ++i)
        res *= a;
    return res;
}

template<
    typename T,
    std::enable_if_t<
        std::is_integral<T>::value &&
        std::is_signed<T>::value, std::nullptr_t> = nullptr>
constexpr T div_ceil(T a, T b) {
    return a/b + (((a<0)^(b>0)) && (a%b));
}

template<
    typename T,
    std::enable_if_t<
        std::is_integral<T>::value &&
        std::is_unsigned<T>::value, std::nullptr_t> = nullptr>
constexpr T div_ceil(T a, T b) {
    return a/b + !!(a%b);
}

template<
    typename T,
    std::enable_if_t<
        std::is_integral<T>::value &&
        std::is_signed<T>::value, std::nullptr_t> = nullptr>
constexpr T div_floor(T a, T b) {
    return a/b - (((a>0)^(b>0)) && (a%b));
}

template<
    typename T,
    std::enable_if_t<
        std::is_integral<T>::value &&
        std::is_unsigned<T>::value, std::nullptr_t> = nullptr>
constexpr T div_floor(T a, T b) {
    return a/b;
}

template<typename T, typename U>
constexpr auto modulo(T a, U b) {
    using R = common_type_t<T,U>;
    assert(0 < b);
    R r = a % b;
    return r >= 0 ? r : r+b;
}

template<typename T>
constexpr T clamp(T x, T lo, T hi) {
    assert(lo <= hi);
    if(x < lo)
        return lo;
    else if(hi < x)
        return hi;
    else
        return x;
}

i64 isqrt(i64 x) {
    assert(x >= 0);

    i64 lo = 0;
    i64 hi = 3037000500LL;
    return bin_search(lo, hi, [x](i64 r) { return r*r <= x; });
}

template<typename T, typename U>
bool chmax(T& xmax, const U& x) {
    if(xmax < x) {
        xmax = x;
        return true;
    }
    else {
        return false;
    }
}

template<typename T, typename U>
bool chmin(T& xmin, const U& x) {
    if(x < xmin) {
        xmin = x;
        return true;
    }
    else {
        return false;
    }
}

template<typename T>
constexpr int SIZE(const T& c) {
    return static_cast<int>(c.size());
}

template<typename T, size_t N>
constexpr int SIZE(const T (&)[N]) {
    return static_cast<int>(N);
}

template<typename InputIt, typename T>
int argfind(InputIt first, InputIt last, const T& x) {
    auto it = find(first, last, x);
    return distance(first, it);
}

template<typename InputIt>
int argmax(InputIt first, InputIt last) {
    auto it = max_element(first, last);
    return distance(first, it);
}

template<typename InputIt>
int argmin(InputIt first, InputIt last) {
    auto it = min_element(first, last);
    return distance(first, it);
}

template<typename InputIt>
bool alltrue(InputIt first, InputIt last) {
    return all_of(first, last, [](bool b) { return b; });
}

template<typename InputIt>
bool anytrue(InputIt first, InputIt last) {
    return any_of(first, last, [](bool b) { return b; });
}

template<typename InputIt>
bool allfalse(InputIt first, InputIt last) {
    return !anytrue(first, last);
}

template<typename InputIt>
bool anyfalse(InputIt first, InputIt last) {
    return !alltrue(first, last);
}

template<typename T>
array<pair<T,T>,4> neighbor4(const T& x, const T& y) {
    return array<pair<T,T>,4> {{
                    { x, y-1 },
        { x-1, y },             { x+1, y },
                    { x, y+1 },
    }};
}

template<typename T>
array<pair<T,T>,8> neighbor8(const T& x, const T& y) {
    return array<pair<T,T>,8> {{
        { x-1, y-1 }, { x, y-1 }, { x+1, y-1 },
        { x-1, y   },             { x+1, y   },
        { x-1, y+1 }, { x, y+1 }, { x+1, y+1 },
    }};
}

template<typename T>
bool in_bounds(const T& x, const T& minx, const T& maxx) {
    return !(x < minx) && !(maxx < x);
}

template<typename T>
bool in_bounds_2(
    const T& x,    const T& y,
    const T& minx, const T& miny,
    const T& maxx, const T& maxy) {
    return in_bounds(x, minx, maxx) && in_bounds(y, miny, maxy);
}

template<typename T>
bool in_bounds_wh(const T& x, const T& y, const T& w, const T& h) {
    return in_bounds_2(x, y, 0, 0, w-1, h-1);
}

struct pairhash {
    template<typename T1, typename T2>
    size_t operator()(const pair<T1,T2>& p) const {
        size_t res = 17;
        res = 31*res + hash<T1>()(p.first);
        res = 31*res + hash<T2>()(p.second);
        return res;
    }
};

struct vectorhash {
    template<typename T>
    size_t operator()(const vector<T>& v) const {
        size_t res = 17;
        res = 31*res + hash<size_t>()(v.size());
        for(const auto& e : v) {
            res = 31*res + hash<T>()(e);
        }
        return res;
    }
};

template<typename K, typename V>
pair<typename map<K,V>::iterator, bool> insert_or_assign(map<K,V>& m, const K& k, const V& v) {
    auto it = m.lower_bound(k);
    if(it != end(m) && !m.key_comp()(k,it->first)) {
        it->second = v;
        return make_pair(it, false);
    }
    else {
        auto it_ins = m.insert(it, make_pair(k,v));
        return make_pair(it_ins, true);
    }
}

template<typename K, typename V>
pair<typename unordered_map<K,V>::iterator, bool>
insert_or_assign(unordered_map<K,V>& m, const K& k, const V& v) {
    auto it = m.find(k);
    if(it != end(m)) {
        it->second = v;
        return make_pair(it, false);
    }
    else {
        auto it_ins = m.insert(it, make_pair(k,v));
        return make_pair(it_ins, true);
    }
}

template<typename T>
string TO_STRING(const T& x) {
    ostringstream out;
    out << x;
    return out.str();
}

template<typename InputIt>
string JOIN(InputIt first, InputIt last, const string& sep) {
    ostringstream out;
    while(first != last) {
        out << *first++;
        if(first != last)
            out << sep;
    }
    return out.str();
}

template<typename InputIt>
auto SUM(InputIt first, InputIt last) {
    using T = typename iterator_traits<InputIt>::value_type;
    return accumulate(first, last, T());
}

template<typename T>
void UNIQ(T& c) {
    c.erase(unique(begin(c), end(c)), end(c));
}

template<typename T, typename F>
enable_if_t<rank<T>::value==0> ARRAY_FOREACH(T& e, F f) {
    f(e);
}

template<typename Array, typename F>
enable_if_t<rank<Array>::value!=0> ARRAY_FOREACH(Array& ary, F f) {
    for(auto& e : ary)
        ARRAY_FOREACH(e, f);
}

template<typename Array, typename U>
enable_if_t<rank<Array>::value!=0> ARRAY_FILL(Array& ary, const U& v) {
    ARRAY_FOREACH(ary, [&v](auto& elem) { elem = v; });
}

template<typename T>
T POP_BACK(vector<T>& que) {
    T x = que.back(); que.pop_back();
    return x;
}

template<typename T>
T POP_BACK(deque<T>& que) {
    T x = que.back(); que.pop_back();
    return x;
}

template<typename T>
T POP_FRONT(deque<T>& que) {
    T x = que.front(); que.pop_front();
    return x;
}

template<typename T, typename C>
T POP(stack<T,C>& stk) {
    T x = stk.top(); stk.pop();
    return x;
}

template<typename T, typename C>
T POP(queue<T,C>& que) {
    T x = que.front(); que.pop();
    return x;
}

template<typename T, typename Cont, typename Cmp>
T POP(priority_queue<T,Cont,Cmp>& que) {
    T x = que.top(); que.pop();
    return x;
}

template<typename T>
void RD(T& x) {
    cin >> x;
#ifdef DEBUG
    if(!cin) assert(false);
#endif
}

template<typename T>
void RD(vector<T>& v, int n) {
    v.reserve(n);
    for(int i = 0; i < n; ++i) {
        T e; RD(e);
        v.emplace_back(e);
    }
}

// 出力 {{{
// FPRINTSEQ {{{
template<typename InputIt>
ostream& FPRINTSEQ(ostream& out, InputIt first, InputIt last) {
    for(InputIt it = first; it != last; ++it) {
        if(it != first) out << ' ';
        out << *it;
    }
    return out;
}
template<typename InputIt>
ostream& PRINTSEQ(InputIt first, InputIt last) {
    return FPRINTSEQ(cout, first, last);
}
template<typename InputIt>
ostream& DPRINTSEQ(InputIt first, InputIt last) {
#ifdef DEBUG
    FPRINTSEQ(cerr, first, last);
#endif
    return cerr;
}
// }}}

// 1次元生配列 {{{
template<typename T, size_t N>
ostream& FPRINTARRAY1(ostream& out, const T (&c)[N]) {
    return FPRINTSEQ(out, cbegin(c), cend(c));
}
template<typename T, size_t N>
ostream& PRINTARRAY1(const T (&c)[N]) {
    return FPRINTARRAY1(cout, c);
}
template<typename T, size_t N>
ostream& DPRINTARRAY1(const T (&c)[N]) {
#ifdef DEBUG
    FPRINTARRAY1(cerr, c);
#endif
    return cerr;
}
// }}}

// 2次元生配列 {{{
template<typename T, size_t N1, size_t N2>
ostream& FPRINTARRAY2(ostream& out, const T (&c)[N1][N2]) {
    out << '\n';
    for(const auto& e : c) {
        FPRINTARRAY1(out, e) << '\n';
    }
    return out;
}
template<typename T, size_t N1, size_t N2>
ostream& PRINTARRAY2(const T (&c)[N1][N2]) {
    return FPRINTARRAY2(cout, c);
}
template<typename T, size_t N1, size_t N2>
ostream& DPRINTARRAY2(const T (&c)[N1][N2]) {
#ifdef DEBUG
    FPRINTARRAY2(cerr, c);
#endif
    return cerr;
}
// }}}

// 非mapコンテナ {{{
template<typename T>
ostream& operator<<(ostream& out, const vector<T>& c) {
    return FPRINTSEQ(out, cbegin(c), cend(c));
}

// 特別扱い
template<typename T>
ostream& operator<<(ostream& out, const vector<vector<T>>& c) {
    out << '\n';
    for(const auto& e : c) {
        out << e << '\n';
    }
    return out;
}

// 特別扱い
ostream& operator<<(ostream& out, const vector<string>& c) {
    out << '\n';
    for(const string& e : c) {
        out << e << '\n';
    }
    return out;
}

template<typename T>
ostream& operator<<(ostream& out, const deque<T>& c) {
    return FPRINTSEQ(out, cbegin(c), cend(c));
}

template<typename T>
ostream& operator<<(ostream& out, const list<T>& c) {
    return FPRINTSEQ(out, cbegin(c), cend(c));
}

template<typename T>
ostream& operator<<(ostream& out, const forward_list<T>& c) {
    return FPRINTSEQ(out, cbegin(c), cend(c));
}

template<typename T>
ostream& operator<<(ostream& out, const set<T>& c) {
    return FPRINTSEQ(out, cbegin(c), cend(c));
}

template<typename T>
ostream& operator<<(ostream& out, const unordered_set<T>& c) {
    return out << set<T>(cbegin(c), cend(c));
}

template<typename T>
ostream& operator<<(ostream& out, const multiset<T>& c) {
    return FPRINTSEQ(out, cbegin(c), cend(c));
}

template<typename T>
ostream& operator<<(ostream& out, const unordered_multiset<T>& c) {
    return out << multiset<T>(cbegin(c), cend(c));
}

template<typename T, size_t N>
ostream& operator<<(ostream& out, const array<T,N>& c) {
    return FPRINTSEQ(out, cbegin(c), cend(c));
}
// }}}

// mapコンテナ {{{
template<typename InputIt>
ostream& FPRINTMAP(ostream& out, InputIt first, InputIt last) {
    out << "{\n";
    for(auto it = first; it != last; ++it) {
        out << "  " << it->first << " : " << it->second << '\n';
    }
    out << "}\n";
    return out;
}
template<typename InputIt>
ostream& PRINTMAP(InputIt first, InputIt last) {
    return FPRINTMAP(cout, first, last);
}
template<typename InputIt>
ostream& DPRINTMAP(InputIt first, InputIt last) {
#ifdef DEBUG
    FPRINTMAP(cerr, first, last);
#endif
    return cerr;
}

template<typename K, typename V>
ostream& operator<<(ostream& out, const map<K,V>& c) {
    return FPRINTMAP(out, cbegin(c), cend(c));
}

template<typename K, typename V>
ostream& operator<<(ostream& out, const unordered_map<K,V>& c) {
    return out << map<K,V>(cbegin(c), cend(c));
}

template<typename K, typename V>
ostream& operator<<(ostream& out, const multimap<K,V>& c) {
    return FPRINTMAP(out, cbegin(c), cend(c));
}

template<typename K, typename V>
ostream& operator<<(ostream& out, const unordered_multimap<K,V>& c) {
    return out << multimap<K,V>(cbegin(c), cend(c));
}
// }}}

// stack/queue/priority_queue {{{
template<typename T, typename C>
ostream& operator<<(ostream& out, stack<T,C> c) {
    while(!c.empty()) {
        out << c.top();
        c.pop();
        if(!c.empty()) out << ' ';
    }
    return out;
}

template<typename T, typename C>
ostream& operator<<(ostream& out, queue<T,C> c) {
    while(!c.empty()) {
        out << c.front();
        c.pop();
        if(!c.empty()) out << ' ';
    }
    return out;
}

template<typename T, typename Cont, typename Cmp>
ostream& operator<<(ostream& out, priority_queue<T,Cont,Cmp> c) {
    while(!c.empty()) {
        out << c.top();
        c.pop();
        if(!c.empty()) out << ' ';
    }
    return out;
}
// }}}

// pair/tuple {{{
template<typename T1, typename T2>
ostream& operator<<(ostream& out, const pair<T1,T2>& p) {
    return out << '(' << p.first << ',' << p.second << ')';
}

template<typename Tuple, size_t Pos>
ostream& FPRINTTUPLE(ostream& out, const Tuple&) {
    return out;
}

template<typename Tuple, size_t Pos, typename T, typename... TS>
ostream& FPRINTTUPLE(ostream& out, const Tuple& t) {
    if(Pos != 0)
        out << ',';
    out << get<Pos>(t);
    return FPRINTTUPLE<Tuple,Pos+1,TS...>(out, t);
}

template<typename... TS>
ostream& operator<<(ostream& out, const tuple<TS...>& t) {
    out << '(';
    FPRINTTUPLE<tuple<TS...>,0,TS...>(out, t);
    out << ')';
    return out;
}
// }}}

// PRINT {{{
ostream& FPRINT(ostream& out) { return out; }

template<typename T, typename... TS>
ostream& FPRINT(ostream& out, const T& x, const TS& ...args) {
    out << x;
    if(sizeof...(args))
        out << ' ';
    return FPRINT(out, args...);
}

template<typename... TS>
ostream& FPRINTLN(ostream& out, const TS& ...args) {
    FPRINT(out, args...);
    return out << '\n';
}

template<typename... TS>
ostream& PRINT(const TS& ...args) {
    return FPRINT(cout, args...);
}

template<typename... TS>
ostream& PRINTLN(const TS& ...args) {
    return FPRINTLN(cout, args...);
}

template<typename... TS>
ostream& DPRINT(const TS& ...args) {
#ifdef DEBUG
    FPRINT(cerr, args...);
#endif
    return cerr;
}

template<typename... TS>
ostream& DPRINTLN(const TS& ...args) {
#ifdef DEBUG
    FPRINTLN(cerr, args...);
#endif
    return cerr;
}
// }}}
// }}}

void FLUSH() {
    if(STDIO_ENABLE)
        fflush(stdout);
    else
        cout.flush();
}

[[noreturn]] void EXIT() {
#ifdef DEBUG
    fflush(stdout);
    fflush(stderr);
    cout.flush();
    cerr.flush();
#else
    FLUSH();
#endif
    //quick_exit(0); // does not work on codeforces
    _Exit(0);
}

struct IoInit {
    IoInit() {
#ifndef DEBUG
        cin.tie(nullptr);
        if(!STDIO_ENABLE)
            ios::sync_with_stdio(false);
#endif
        cout << fixed << setprecision(IOS_PREC);

        if(AUTOFLUSH) {
            if(STDIO_ENABLE)
                setvbuf(stdout, nullptr, _IONBF, 0);
            cout << unitbuf;
        }
    }
} IOINIT;

#define FOR(i, start, end) for(i64 i = (start); i < (end); ++i)
#define REP(i, n) FOR(i, 0, n)

#define ALL(f,c,...) (([&](decltype((c)) cc) { return (f)(begin(cc), end(cc), ## __VA_ARGS__); })(c))

#define GENERIC(f) ([](auto&&... args) -> decltype(auto) { return (f)(forward<decltype(args)>(args)...); })

#define MEMSET(a,v) memset((a), (v), sizeof(a))

#define DBG(x) DPRINTLN('L', __LINE__, ':', #x, ':', (x))
// }}}

struct Node {
    i64 parent;
    i64 dist;
    Node(i64 p, i64 d) : parent(p), dist(d) {}
};
ostream& operator<<(ostream& out, const Node& node) {
    return out << "(" << node.parent << "," << node.dist << ")";
}

/**
 * 重み付きUnionFind
 *
 * 検証用問題:
 *
 * * atcoder ARC090 D - People on a Line
 *   https://beta.atcoder.jp/contests/arc090/tasks/arc090_b
 * * AOJ 1330 - Never Wait for Weights
 *   http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1330
 */
class WeightedUnionFind {
public:
    vector<i64> p;     // 親ノード。ただし根の場合 -(集合の要素数)
    vector<i64> w;     // 親ノードに対する重み(負の可能性もある)。根の場合0
    i64         n_set; // 集合の個数

    WeightedUnionFind(i64 n) : p(n, -1), w(n, 0), n_set(n) {}

    i64 node_count() const { return SIZE(p); }

    // 集合の個数
    i64 set_count() const { return n_set; }

    // xが属する集合のサイズ
    i64 set_size(i64 x) { return -p[root(x)]; }

    bool is_root(i64 x) const { return p[x] < 0; }

    i64 root(i64 x) {
        i64 res; tie(res,ignore) = compress(x);
        return res;
    }

    // 根に対する重み
    i64 weight(i64 x) {
        i64 res; tie(ignore,res) = compress(x);
        return res;
    }

    // x, y を併合する
    // x に対する y の重みを d とする
    // 併合できた場合 true を返す。矛盾が生じて併合不能なら false を返す
    // x, y が元々同一集合に属し、かつ d が不適切な値の場合矛盾が生じうる
    bool unite(i64 x, i64 y, i64 d) {
        i64 rx = root(x);
        i64 ry = root(y);
        i64 wx = weight(x);
        i64 wy = weight(y);

        // 元々同一集合の場合、矛盾をチェックするだけ
        if(rx == ry) {
            return wx + d == wy;
        }

        // x, y が異なる集合に属する場合、矛盾は生じない
        // 要素数が大きい方を根とするため、必要ならswap処理
        if(set_size(rx) < set_size(ry)) {
            swap(rx, ry);
            swap(wx, wy);
            d *= -1;
        }
        // rx を根とする
        // rx に対する x の重みは wx
        // ry に対する y の重みは wy
        // x に対する y の重みは d
        // よって、rx に対する ry の重み w[ry] に関して以下が成立:
        // wx + d = w[ry] + wy
        p[rx] += p[ry];       // 要素数を加算
        p[ry]  = rx;          // rx を ry の親にする
        w[ry]  = wx - wy + d; // rx に対する ry の重み

        return true;
    }

    // 同一集合に属するか
    bool same(i64 x, i64 y) {
        return root(x) == root(y);
    }

private:
    // 経路圧縮
    // (xの根、根に対するxの重み) を返す
    tuple<i64,i64> compress(i64 x) {
        if(is_root(x)) return make_tuple(x, 0);

        i64 r,d; tie(r,d) = compress(p[x]);
        p[x]  = r;
        w[x] += d;
        return make_tuple(r, w[x]);
    }
};


i64 N;
i64 M;

void no() {
    PRINTLN("No");
    EXIT();
}

void solve() {
    WeightedUnionFind uf(N);
    DBG(uf.p);
    DBG(uf.w);

    REP(_, M) {
        i64 l,r; RD(l); RD(r); --l; --r; // 0-based
        i64 d;   RD(d);
        if(!uf.unite(l, r, d)) no();
        DBG(uf.p);
        DBG(uf.w);
    }

    PRINTLN("Yes");
}

signed main(signed /*argc*/, char** /*argv*/) {
    RD(N);
    RD(M);

    

    solve();

    EXIT();
}


Measured memory_bytes: 1920