#line 1 "/Users/nok0/Documents/Programming/nok0/atcoder/lazysegtree.hpp"



#include <algorithm>
#include <cassert>
#include <iostream>
#include <vector>

#line 1 "/Users/nok0/Documents/Programming/nok0/atcoder/internal_bit.hpp"



#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
constexpr int bsf_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x))) x++;
    return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}

}  // namespace internal

}  // namespace atcoder


#line 10 "/Users/nok0/Documents/Programming/nok0/atcoder/lazysegtree.hpp"

namespace atcoder {

template <class S,
          S (*op)(S, S),
          S (*e)(),
          class F,
          S (*mapping)(F, S),
          F (*composition)(F, F),
          F (*id)()>
struct lazy_segtree {
  public:
    lazy_segtree() : lazy_segtree(0) {}
    explicit lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}
    explicit lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) {
        log = internal::ceil_pow2(_n);
        size = 1 << log;
        d = std::vector<S>(2 * size, e());
        lz = std::vector<F>(size, id());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    S get(int p) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        return d[p];
    }

    S prod(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return e();

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        S sml = e(), smr = e();
        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }

        return op(sml, smr);
    }

    S all_prod() { return d[1]; }

    void apply(int p, F f) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = mapping(f, d[p]);
        for (int i = 1; i <= log; i++) update(p >> i);
    }
    void apply(int l, int r, F f) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return;

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        {
            int l2 = l, r2 = r;
            while (l < r) {
                if (l & 1) all_apply(l++, f);
                if (r & 1) all_apply(--r, f);
                l >>= 1;
                r >>= 1;
            }
            l = l2;
            r = r2;
        }

        for (int i = 1; i <= log; i++) {
            if (((l >> i) << i) != l) update(l >> i);
            if (((r >> i) << i) != r) update((r - 1) >> i);
        }
    }

    template <bool (*g)(S)> int max_right(int l) {
        return max_right(l, [](S x) { return g(x); });
    }
    template <class G> int max_right(int l, G g) {
        assert(0 <= l && l <= _n);
        assert(g(e()));
        if (l == _n) return _n;
        l += size;
        for (int i = log; i >= 1; i--) push(l >> i);
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!g(op(sm, d[l]))) {
                while (l < size) {
                    push(l);
                    l = (2 * l);
                    if (g(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*g)(S)> int min_left(int r) {
        return min_left(r, [](S x) { return g(x); });
    }
    template <class G> int min_left(int r, G g) {
        assert(0 <= r && r <= _n);
        assert(g(e()));
        if (r == 0) return 0;
        r += size;
        for (int i = log; i >= 1; i--) push((r - 1) >> i);
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!g(op(d[r], sm))) {
                while (r < size) {
                    push(r);
                    r = (2 * r + 1);
                    if (g(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

  private:
    int _n, size, log;
    std::vector<S> d;
    std::vector<F> lz;

    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
    void all_apply(int k, F f) {
        d[k] = mapping(f, d[k]);
        if (k < size) lz[k] = composition(f, lz[k]);
    }
    void push(int k) {
        all_apply(2 * k, lz[k]);
        all_apply(2 * k + 1, lz[k]);
        lz[k] = id();
    }
};

}  // namespace atcoder


#line 1 "/Users/nok0/Documents/Programming/nok0/atcoder/segtree.hpp"



#line 7 "/Users/nok0/Documents/Programming/nok0/atcoder/segtree.hpp"

#line 9 "/Users/nok0/Documents/Programming/nok0/atcoder/segtree.hpp"

namespace atcoder {

template <class S, S (*op)(S, S), S (*e)()> struct segtree {
  public:
    segtree() : segtree(0) {}
    explicit segtree(int n) : segtree(std::vector<S>(n, e())) {}
    explicit segtree(const std::vector<S>& v) : _n(int(v.size())) {
        log = internal::ceil_pow2(_n);
        size = 1 << log;
        d = std::vector<S>(2 * size, e());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    S get(int p) const {
        assert(0 <= p && p < _n);
        return d[p + size];
    }

    S prod(int l, int r) const {
        assert(0 <= l && l <= r && r <= _n);
        S sml = e(), smr = e();
        l += size;
        r += size;

        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }
        return op(sml, smr);
    }

    S all_prod() const { return d[1]; }

    template <bool (*f)(S)> int max_right(int l) const {
        return max_right(l, [](S x) { return f(x); });
    }
    template <class F> int max_right(int l, F f) const {
        assert(0 <= l && l <= _n);
        assert(f(e()));
        if (l == _n) return _n;
        l += size;
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(op(sm, d[l]))) {
                while (l < size) {
                    l = (2 * l);
                    if (f(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*f)(S)> int min_left(int r) const {
        return min_left(r, [](S x) { return f(x); });
    }
    template <class F> int min_left(int r, F f) const {
        assert(0 <= r && r <= _n);
        assert(f(e()));
        if (r == 0) return 0;
        r += size;
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(op(d[r], sm))) {
                while (r < size) {
                    r = (2 * r + 1);
                    if (f(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

  private:
    int _n, size, log;
    std::vector<S> d;

    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};

}  // namespace atcoder


#line 1 "/Users/nok0/Documents/Programming/nok0/cftemp.hpp"
#include <bits/stdc++.h>
using namespace std;

#pragma region Macros
// rep macro
#define foa(v, a) for(auto &v : a)
#define REPname(a, b, c, d, e, ...) e
#define REP(...) REPname(__VA_ARGS__, REP3, REP2, REP1, REP0)(__VA_ARGS__)
#define REP0(x) for(int i = 0; i < (x); ++i)
#define REP1(i, x) for(int i = 0; i < (x); ++i)
#define REP2(i, l, r) for(int i = (l); i < (r); ++i)
#define REP3(i, l, r, c) for(int i = (l); i < (r); i += (c))
#define REPSname(a, b, c, ...) c
#define REPS(...) REPSname(__VA_ARGS__, REPS1, REPS0)(__VA_ARGS__)
#define REPS0(x) for(int i = 1; i <= (x); ++i)
#define REPS1(i, x) for(int i = 1; i <= (x); ++i)
#define RREPname(a, b, c, d, e, ...) e
#define RREP(...) RREPname(__VA_ARGS__, RREP3, RREP2, RREP1, RREP0)(__VA_ARGS__)
#define RREP0(x) for(int i = (x)-1; i >= 0; --i)
#define RREP1(i, x) for(int i = (x)-1; i >= 0; --i)
#define RREP2(i, r, l) for(int i = (r)-1; i >= (l); --i)
#define RREP3(i, r, l, c) for(int i = (r)-1; i >= (l); i -= (c))
#define RREPSname(a, b, c, ...) c
#define RREPS(...) RREPSname(__VA_ARGS__, RREPS1, RREPS0)(__VA_ARGS__)
#define RREPS0(x) for(int i = (x); i >= 1; --i)
#define RREPS1(i, x) for(int i = (x); i >= 1; --i)

// name macro
#define pb push_back
#define eb emplace_back
#define SZ(x) ((int)(x).size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define popcnt(x) __builtin_popcountll(x)
template <class T = int>
using V = std::vector<T>;
template <class T = int>
using VV = std::vector<std::vector<T>>;
template <class T>
using pqup = std::priority_queue<T, std::vector<T>, std::greater<T>>;
using ll = long long;
using ld = long double;
using int128 = __int128_t;
using pii = std::pair<int, int>;
using pll = std::pair<long long, long long>;

// input macro
template <class T, class U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
	is >> p.first >> p.second;
	return is;
}
template <class T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
	for(T &i : v) is >> i;
	return is;
}
std::istream &operator>>(std::istream &is, __int128_t &a) {
	std::string s;
	is >> s;
	__int128_t ret = 0;
	for(int i = 0; i < s.length(); i++)
		if('0' <= s[i] and s[i] <= '9')
			ret = 10 * ret + s[i] - '0';
	a = ret * (s[0] == '-' ? -1 : 1);
	return is;
}
namespace scanner {
void scan(int &a) { std::cin >> a; }
void scan(long long &a) { std::cin >> a; }
void scan(std::string &a) { std::cin >> a; }
void scan(char &a) { std::cin >> a; }
void scan(char a[]) { std::scanf("%s", a); }
void scan(double &a) { std::cin >> a; }
void scan(long double &a) { std::cin >> a; }
template <class T, class U>
void scan(std::pair<T, U> &p) { std::cin >> p; }
template <class T>
void scan(std::vector<T> &a) { std::cin >> a; }
void INPUT() {}
template <class Head, class... Tail>
void INPUT(Head &head, Tail &... tail) {
	scan(head);
	INPUT(tail...);
}
}  // namespace scanner
#define VEC(type, name, size)     \
	std::vector<type> name(size); \
	scanner::INPUT(name)
#define VVEC(type, name, h, w)                                    \
	std::vector<std::vector<type>> name(h, std::vector<type>(w)); \
	scanner::INPUT(name)
#define INT(...)     \
	int __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define LL(...)            \
	long long __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define STR(...)             \
	std::string __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define CHAR(...)     \
	char __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define DOUBLE(...)     \
	double __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define LD(...)              \
	long double __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)

// output-macro
template <class T, class U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
	os << p.first << " " << p.second;
	return os;
}
template <class T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &a) {
	for(int i = 0; i < int(a.size()); ++i) {
		if(i) os << " ";
		os << a[i];
	}
	return os;
}
std::ostream &operator<<(std::ostream &dest, __int128_t &value) {
	std::ostream::sentry s(dest);
	if(s) {
		__uint128_t tmp = value < 0 ? -value : value;
		char buffer[128];
		char *d = std::end(buffer);
		do {
			--d;
			*d = "0123456789"[tmp % 10];
			tmp /= 10;
		} while(tmp != 0);
		if(value < 0) {
			--d;
			*d = '-';
		}
		int len = std::end(buffer) - d;
		if(dest.rdbuf()->sputn(d, len) != len) {
			dest.setstate(std::ios_base::badbit);
		}
	}
	return dest;
}
template <class T>
void print(const T a) { std::cout << a << '\n'; }
template <class Head, class... Tail>
void print(Head H, Tail... T) {
	std::cout << H << ' ';
	print(T...);
}
template <class T>
void printel(const T a) { std::cout << a << '\n'; }
template <class T>
void printel(const std::vector<T> &a) {
	for(const auto &v : a)
		std::cout << v << '\n';
}
template <class Head, class... Tail>
void printel(Head H, Tail... T) {
	std::cout << H << '\n';
	printel(T...);
}
void Yes(const bool b = true) { std::cout << (b ? "Yes\n" : "No\n"); }
void No() { std::cout << "No\n"; }
void YES(const bool b = true) { std::cout << (b ? "YES\n" : "NO\n"); }
void NO() { std::cout << "NO\n"; }
void err(const bool b = true) {
	if(b) {
		std::cout << "-1\n", exit(0);
	}
}

//debug macro
namespace debugger {
template <class T>
void view(const std::vector<T> &a) {
	std::cerr << "{ ";
	for(const auto &v : a) {
		std::cerr << v << ", ";
	}
	std::cerr << "\b\b }";
}
template <class T>
void view(const std::vector<std::vector<T>> &a) {
	std::cerr << "{\n";
	for(const auto &v : a) {
		std::cerr << "\t";
		view(v);
		std::cerr << "\n";
	}
	std::cerr << "}";
}
template <class T, class U>
void view(const std::vector<std::pair<T, U>> &a) {
	std::cerr << "{\n";
	for(const auto &p : a) std::cerr << "\t(" << p.first << ", " << p.second << ")\n";
	std::cerr << "}";
}
template <class T, class U>
void view(const std::map<T, U> &m) {
	std::cerr << "{\n";
	for(const auto &p : m) std::cerr << "\t[" << p.first << "] : " << p.second << "\n";
	std::cerr << "}";
}
template <class T, class U>
void view(const std::pair<T, U> &p) { std::cerr << "(" << p.first << ", " << p.second << ")"; }
template <class T>
void view(const std::set<T> &s) {
	std::cerr << "{ ";
	for(auto &v : s) {
		view(v);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <class T>
void view(const T &e) { std::cerr << e; }
}  // namespace debugger
#ifdef LOCAL
void debug_out() {}
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
	debugger::view(H);
	std::cerr << ", ";
	debug_out(T...);
}
#define debug(...)                                                \
	do {                                                          \
		std::cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \
		debug_out(__VA_ARGS__);                                   \
		std::cerr << "\b\b]\n";                                   \
	} while(false)
#else
#define debug(...) (void(0))
#endif

// vector macro
template <class T>
int lb(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::lower_bound((a).begin(), (a).end(), (x))); }
template <class T>
int ub(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::upper_bound((a).begin(), (a).end(), (x))); }
template <class T>
void UNIQUE(std::vector<T> &a) {
	std::sort(a.begin(), a.end());
	a.erase(std::unique(a.begin(), a.end()), a.end());
}
template <class T>
std::vector<T> press(std::vector<T> &a) {
	auto res = a;
	UNIQUE(res);
	for(auto &v : a)
		v = lb(res, v);
	return res;
}
#define SORTname(a, b, c, ...) c
#define SORT(...) SORTname(__VA_ARGS__, SORT1, SORT0, ...)(__VA_ARGS__)
#define SORT0(a) std::sort((a).begin(), (a).end())
#define SORT1(a, c) std::sort((a).begin(), (a).end(), [](const auto x, const auto y) { return x c y; })
template <class T>
void ADD(std::vector<T> &a, const T x = 1) {
	for(auto &v : a) v += x;
}
template <class T>
void SUB(std::vector<T> &a, const T x = 1) {
	for(auto &v : a) v -= x;
}
template <class T>
void MUL(std::vector<T> &a, const T x) {
	for(auto &v : a) v *= x;
}
template <class T>
void DIV(std::vector<T> &a, const T x) {
	for(auto &v : a) v /= x;
}
std::vector<std::pair<char, int>> rle(const string &s) {
	int n = s.size();
	std::vector<std::pair<char, int>> ret;
	for(int l = 0; l < n;) {
		int r = l + 1;
		for(; r < n and s[l] == s[r]; r++) {}
		ret.emplace_back(s[l], r - l);
		l = r;
	}
	return ret;
}
template <class T>
std::vector<std::pair<T, int>> rle(const std::vector<T> &v) {
	int n = v.size();
	std::vector<std::pair<T, int>> ret;
	for(int l = 0; l < n;) {
		int r = l + 1;
		for(; r < n and v[l] == v[r]; r++) {}
		ret.emplace_back(v[l], r - l);
		l = r;
	}
	return ret;
}

// math macro
template <class T, class U>
inline bool chmin(T &a, const U &b) { return a > b ? a = b, true : false; }
template <class T, class U>
inline bool chmax(T &a, const U &b) { return a < b ? a = b, true : false; }
template <class T>
T divup(T x, T y) { return (x + y - 1) / y; }
template <class T>
T POW(T a, long long n) {
	T ret = 1;
	while(n) {
		if(n & 1) ret *= a;
		a *= a;
		n >>= 1;
	}
	return ret;
}
// modpow
long long POW(long long a, long long n, const int mod) {
	long long ret = 1;
	a = (a % mod + mod) % mod;
	while(n) {
		if(n & 1) (ret *= a) %= mod;
		(a *= a) %= mod;
		n >>= 1;
	}
	return ret;
}

// others
struct fast_io {
	fast_io() {
		ios::sync_with_stdio(false);
		cin.tie(nullptr);
		cout << fixed << setprecision(15);
	}
} fast_io_;
const int inf = 1e9;
const ll INF = 1e18;
#pragma endregion

void main_();

int main() {
	main_();
	return 0;
}
#line 4 "d.cpp"

#pragma region datastructure Segment Tree Beats
#line 7 "d.cpp"

template <class T>
struct SegmentTreeBeats {
private:
	size_t n, n_;
	const T MAX = std::numeric_limits<T>::max();
	const T MIN = -MAX;
	std::vector<T> max_v, min_v, smax_v, smin_v, lz_upd, lz_ad, sigm, len;
	std::vector<int> max_c, min_c;

	void init(std::vector<T> &v) {
		n_ = v.size(), n = 1;
		while(n < n_) n *= 2;
		max_v.assign(n * 2 - 1, MIN);
		min_v.assign(n * 2 - 1, MAX);
		smax_v.assign(n * 2 - 1, MIN);
		smin_v.assign(n * 2 - 1, MAX);
		lz_upd.assign(n * 2 - 1, MAX);
		lz_ad.assign(n * 2 - 1, 0);
		len.assign(n * 2 - 1, n);
		sigm.assign(n * 2 - 1, 0);
		max_c.assign(n * 2 - 1, 1);
		min_c.assign(n * 2 - 1, 1);

		for(int i = 0; i < n - 1; i++)
			len[i * 2 + 1] = len[i * 2 + 2] = (len[i] >> 1);

		for(int i = 0; i < n_; i++)
			max_v[i + n - 1] = min_v[i + n - 1] = sigm[i + n - 1] = v[i];

		for(int i = n - 2; i >= 0; i--)
			proc(i);
	}

	void proc(int i) {
		sigm[i] = sigm[i * 2 + 1] + sigm[i * 2 + 2];

		max_v[i] = std::max(max_v[i * 2 + 1], max_v[i * 2 + 2]);

		if(max_v[i * 2 + 1] > max_v[i * 2 + 2]) {
			max_c[i] = max_c[i * 2 + 1];
			smax_v[i] = std::max(smax_v[i * 2 + 1], max_v[i * 2 + 2]);
		}

		if(max_v[i * 2 + 1] < max_v[i * 2 + 2]) {
			max_c[i] = max_c[i * 2 + 2];
			smax_v[i] = std::max(max_v[i * 2 + 1], smax_v[i * 2 + 2]);
		}

		if(max_v[i * 2 + 1] == max_v[i * 2 + 2]) {
			max_c[i] = max_c[i * 2 + 1] + max_c[i * 2 + 2];
			smax_v[i] = std::max(smax_v[i * 2 + 1], smax_v[i * 2 + 2]);
		}

		min_v[i] = std::min(min_v[i * 2 + 1], min_v[i * 2 + 2]);

		if(min_v[i * 2 + 1] < min_v[i * 2 + 2]) {
			min_c[i] = min_c[i * 2 + 1];
			smin_v[i] = std::min(smin_v[i * 2 + 1], min_v[i * 2 + 2]);
		}

		if(min_v[i * 2 + 1] > min_v[i * 2 + 2]) {
			min_c[i] = min_c[i * 2 + 2];
			smin_v[i] = std::min(min_v[i * 2 + 1], smin_v[i * 2 + 2]);
		}

		if(min_v[i * 2 + 1] == min_v[i * 2 + 2]) {
			min_c[i] = min_c[i * 2 + 1] + min_c[i * 2 + 2];
			smin_v[i] = std::min(smin_v[i * 2 + 1], smin_v[i * 2 + 2]);
		}
	}

	void eval(int i) {
		if(lz_upd[i] != MAX) {
			in_update(i * 2 + 1, lz_upd[i]);
			in_update(i * 2 + 2, lz_upd[i]);
			lz_upd[i] = MAX;
			return;
		}

		if(lz_ad[i]) {
			in_add(i * 2 + 1, lz_ad[i]);
			in_add(i * 2 + 2, lz_ad[i]);
			lz_ad[i] = 0;
		}

		if(max_v[i] < max_v[i * 2 + 1]) in_chmin(i * 2 + 1, max_v[i]);
		if(max_v[i] < max_v[i * 2 + 2]) in_chmin(i * 2 + 2, max_v[i]);

		if(min_v[i] > min_v[i * 2 + 1]) in_chmax(i * 2 + 1, min_v[i]);
		if(min_v[i] > min_v[i * 2 + 2]) in_chmax(i * 2 + 2, min_v[i]);
	}

	void in_update(int i, T x) {
		max_v[i] = min_v[i] = x;
		smax_v[i] = MIN, smin_v[i] = MAX;
		max_c[i] = min_c[i] = len[i];
		sigm[i] = len[i] * x;
		lz_upd[i] = x, lz_ad[i] = 0;
	}

	void in_chmin(int i, T x) {
		sigm[i] += (x - max_v[i]) * max_c[i];

		if(max_v[i] == min_v[i])
			max_v[i] = min_v[i] = x;

		else if(max_v[i] == smin_v[i])
			max_v[i] = smin_v[i] = x;

		else
			max_v[i] = x;

		if(lz_upd[i] != MAX and lz_upd[i] > x) lz_upd[i] = x;
	}

	void in_chmax(int i, T x) {
		sigm[i] += (x - min_v[i]) * min_c[i];

		if(min_v[i] == max_v[i])
			min_v[i] = max_v[i] = x;

		else if(min_v[i] == smax_v[i])
			min_v[i] = smax_v[i] = x;

		else
			min_v[i] = x;

		if(lz_upd[i] != MAX and lz_upd[i] < x) lz_upd[i] = x;
	}

	void in_add(int i, T x) {
		max_v[i] += x, min_v[i] += x;

		if(smin_v[i] != MAX) smin_v[i] += x;
		if(smax_v[i] != MIN) smax_v[i] += x;

		sigm[i] += x * len[i];

		if(lz_upd[i] != MAX) lz_upd[i] += x;
		lz_ad[i] += x;
	}

	void chmin(int i, int a, int b, int l, int r, T x) {
		if(b <= l or r <= a or x >= max_v[i]) return;

		if(a <= l and r <= b and smax_v[i] < x) {
			in_chmin(i, x);
			return;
		}

		eval(i);
		chmin(i * 2 + 1, a, b, l, (l + r) >> 1, x);
		chmin(i * 2 + 2, a, b, (l + r) >> 1, r, x);
		proc(i);
	}

	void chmax(int i, int a, int b, int l, int r, T x) {
		if(b <= l or r <= a or x <= min_v[i]) return;

		if(a <= l and r <= b and smin_v[i] > x) {
			in_chmax(i, x);
			return;
		}

		eval(i);
		chmax(i * 2 + 1, a, b, l, (l + r) >> 1, x);
		chmax(i * 2 + 2, a, b, (l + r) >> 1, r, x);
		proc(i);
	}

	void add(int i, int a, int b, int l, int r, T x) {
		if(b <= l or r <= a) return;

		if(a <= l and r <= b) {
			in_add(i, x);
			return;
		}

		eval(i);
		add(i * 2 + 1, a, b, l, (l + r) >> 1, x);
		add(i * 2 + 2, a, b, (l + r) >> 1, r, x);
		proc(i);
	}

	void update(int i, int a, int b, int l, int r, T x) {
		if(b <= l or r <= a) return;

		if(a <= l and r <= b) {
			in_update(i, x);
			return;
		}

		eval(i);
		update(i * 2 + 1, a, b, l, (l + r) >> 1, x);
		update(i * 2 + 2, a, b, (l + r) >> 1, r, x);
		proc(i);
	}

	T sum(int i, int a, int b, int l, int r) {
		if(r <= a || b <= l) return 0;

		if(a <= l && r <= b) return sigm[i];

		eval(i);
		T lv = sum(i * 2 + 1, a, b, l, (l + r) / 2);
		T rv = sum(i * 2 + 2, a, b, (l + r) / 2, r);
		return lv + rv;
	}

	T rangemin(int i, int a, int b, int l, int r) {
		if(r <= a or b <= l) return MAX;

		if(a <= l and r <= b) return min_v[i];

		eval(i);
		T lv = rangemin(i * 2 + 1, a, b, l, (l + r) >> 1);
		T rv = rangemin(i * 2 + 2, a, b, (l + r) >> 1, r);
		return std::min(lv, rv);
	}

	T rangemax(int i, int a, int b, int l, int r) {
		if(r <= a or b <= l) return MIN;

		if(a <= l and r <= b) return max_v[i];

		eval(i);
		T lv = rangemax(i * 2 + 1, a, b, l, (l + r) >> 1);
		T rv = rangemax(i * 2 + 2, a, b, (l + r) >> 1, r);
		return std::max(lv, rv);
	}

	T rangesum(int i, int a, int b, int l, int r) {
		if(r <= a or b <= l) return 0;

		if(a <= l and r <= b) return sigm[i];

		eval(i);
		T lv = rangesum(i * 2 + 1, a, b, l, (l + r) >> 1);
		T rv = rangesum(i * 2 + 2, a, b, (l + r) >> 1, r);
		return lv + rv;
	}

public:
	SegmentTreeBeats() = default;

	SegmentTreeBeats(std::vector<T> &v) {
		init(v);
	}

	SegmentTreeBeats(size_t n, T init_data = 0) {
		std::vector<T> v(n, init_data);
		init(v);
	}

	T operator[](int i) {
		return query_min(i, i + 1);
	}

	void update_chmin(int a, int b, T x) {
		chmin(0, a, b, 0, n, x);
	}

	void update_chmax(int a, int b, T x) {
		chmax(0, a, b, 0, n, x);
	}

	void update_add(int a, int b, T x) {
		add(0, a, b, 0, n, x);
	}

	void update_upd(int a, int b, T x) {
		update(0, a, b, 0, n, x);
	}

	T query_min(int a, int b) {
		return rangemin(0, a, b, 0, n);
	}

	T query_max(int a, int b) {
		return rangemax(0, a, b, 0, n);
	}

	T query_sum(int a, int b) {
		return rangesum(0, a, b, 0, n);
	}
};
#pragma endregion

using S = int;
S op(S x, S y) { return min(x, y); }
S e() { return inf; }

using F = int;

S mapping(F f, S x) { return f + x; }
F composition(F f, F g) { return f + g; }
F id() { return 0; }

void main_() {
	INT(n, q);
	map<int, V<pii>> mp;
	atcoder::lazy_segtree<S, op, e, F, mapping, composition, id> seg(V<>(n, 0));
	REP(i, q) {
		INT(l, r, b);
		--l;
		seg.apply(l, r, 1);
		mp[b].eb(l, r);
	}
	atcoder::segtree<S, op, e> rmq(n);

	set<int> exi;
	REP(i, n) { exi.insert(i); }
	exi.insert(inf);
	for(auto [val, vec] : mp) {
		for(auto [l, r] : vec) {
			seg.apply(l, r, -1);
		}
		for(auto [l, r] : vec) {
			if(seg.prod(l, r) > 0) {
				print(-1);
				return;
			}
			if(rmq.prod(l, r) == val) {
				continue;
			}
			int ok = r, ng = l;
			while(abs(ok - ng) > 1) {
				int mid = (ok + ng) / 2;
				if(seg.prod(l, mid) == 0)
					ok = mid;
				else
					ng = mid;
			}
			rmq.set(ok - 1, val);
		}
	}
	V<> res;
	REP(i, n) { res.pb(rmq.get(i)); }
	print(res);
}