Problem:
Single Source Shortest Path

For a given weighted graph G(V, E) and a source r, find the source shortest path to each vertex from the source (SSSP: Single Source Shortest Path).

Input

An edge-weighted graph G (V, E) and the source r.

|V| |E| r
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1

|V| is the number of vertices and |E| is the number of edges in G. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively. r is the source of the graph.

si and ti represent source and target vertices of i-th edge (directed) and di represents the cost of the i-th edge.

Output

Print the costs of SSSP in the following format.

c0
c1
:
c|V|-1

The output consists of |V| lines. Print the cost of the shortest path from the source r to each vertex 0, 1, ... |V|-1 in order. If there is no path from the source to a vertex, print INF.

Constraints

1 ≤ |V| ≤ 100000

0 ≤ di ≤ 10000

0 ≤ |E| ≤ 500000

There are no parallel edges

There are no self-loops

Sample Input 1

4 5 0
0 1 1
0 2 4
1 2 2
2 3 1
1 3 5

Sample Output 1

0
1
3
4

Sample Input 2

4 6 1
0 1 1
0 2 4
2 0 1
1 2 2
3 1 1
3 2 5

Sample Output 2

3
0
2
INF

Solution in JAVA (judge verdict: Wrong Answer)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashMap;
import java.util.Map.Entry;
import java.util.NoSuchElementException;
import java.util.TreeMap;
import java.util.TreeSet;

// Unordered Pair
class UP<A, B> {
	A a;
	B b;

	UP(A a, B b) {
		this.a = a;
		this.b = b;
	}

	static <A, B> UP<A, B> make(A a, B b) {
		return new UP<A, B>(a, b);
	}

	public UP<A, B> clone() {
		return make(a, b);
	}

	public boolean equals(Object o) {
		if (o == this)
			return true;
		if (!(o instanceof UP))
			return false;
		UP<?, ?> p = (UP<?, ?>) o;
		boolean aok = a == null ? p.a == null : a.equals(p.a);
		boolean bok = b == null ? p.b == null : b.equals(p.b);
		return aok && bok;
	}

	public String toString() {
		return "(" + a.toString() + ", " + b.toString() + ")";
	}
}

// Pair
class P<A extends Comparable<A>, B extends Comparable<B>> extends UP<A, B> implements Comparable<P<A, B>> {
	P(A a, B b) {
		super(a, b);
	}

	static <A extends Comparable<A>, B extends Comparable<B>> P<A, B> make(A a, B b) {
		return new P<A, B>(a, b);
	}

	public int compareTo(P<A, B> o) {
		int sa = a.compareTo(o.a);
		int sb = b.compareTo(o.b);
		return sa != 0 ? sa : sb;
	}

	public P<A, B> clone() {
		return make(a, b);
	}
}

// Unordered Tuple
class UT<A, B, C> {
	A a;
	B b;
	C c;

	UT(A a, B b, C c) {
		this.a = a;
		this.b = b;
		this.c = c;
	}

	static <A, B, C> UT<A, B, C> make(A a, B b, C c) {
		return new UT<A, B, C>(a, b, c);
	}

	public UT<A, B, C> clone() {
		return make(a, b, c);
	}

	public boolean equals(Object o) {
		if (o == this)
			return true;
		if (!(o instanceof UT))
			return false;
		UT<?, ?, ?> t = (UT<?, ?, ?>) o;
		boolean aok = a == null ? t.a == null : a.equals(t.a);
		boolean bok = b == null ? t.b == null : b.equals(t.b);
		boolean cok = c == null ? t.c == null : c.equals(t.c);
		return aok && bok && cok;
	}

	public String toString() {
		return "(" + a.toString() + ", " + b.toString() + ", " + c.toString() + ")";
	}
}

// Tuple
class T<A extends Comparable<A>, B extends Comparable<B>, C extends Comparable<C>> extends UT<A, B, C> implements
		Comparable<T<A, B, C>> {
	private T(A a, B b, C c) {
		super(a, b, c);
	}

	static <A extends Comparable<A>, B extends Comparable<B>, C extends Comparable<C>> T<A, B, C> make(A a, B b, C c) {
		return new T<A, B, C>(a, b, c);
	}

	public int compareTo(T<A, B, C> o) {
		int sa = a.compareTo(o.a);
		int sb = b.compareTo(o.b);
		int sc = c.compareTo(o.c);
		return sa != 0 ? sa : sb != 0 ? sb : sc;
	}

	public T<A, B, C> clone() {
		return make(a, b, c);
	}
}

interface F1<A> {
	A f();
}

interface F2<A, B> {
	B f(A a);
}

interface F3<A, B, C> {
	C f(A a, B b);
}

interface F4<A, B, C, D> {
	D f(A a, B b, C c);
}

interface F5<A, B, C, D, E> {
	E f(A a, B b, C c, D d);
}

interface F1V<A> {
	void f(A a);
}

interface F2V<A, B> {
	void f(A a, B b);
}

interface F3V<A, B, C> {
	void f(A a, B b, C c);
}

interface F4V<A, B, C, D> {
	void f(A a, B b, C c, D d);
}

interface F5V<A, B, C, D, E> {
	void f(A a, B b, C c, D d, E e);
}

// Utilities
class U {
	static <A> ArrayList<A> make(int n, F2<Integer, A> maker) {
		ArrayList<A> res = new ArrayList<A>();
		for (int i = 0; i < n; i++)
			res.add(maker.f(i));
		return res;
	}

	static <A> ArrayList<A> filter(ArrayList<A> as, F2<A, Boolean> pred) {
		ArrayList<A> res = new ArrayList<A>();
		for (A a : as)
			if (pred.f(a))
				res.add(a);
		return res;
	}

	static <A> int count(ArrayList<A> as, F2<A, Boolean> pred) {
		int res = 0;
		for (A a : as)
			if (pred.f(a))
				res++;
		return res;
	}

	static <A> ArrayList<A> concat(ArrayList<A> as, ArrayList<A> bs) {
		ArrayList<A> res = new ArrayList<A>();
		res.addAll(as);
		res.addAll(bs);
		return res;
	}

	static <A> boolean any(ArrayList<A> as, F2<A, Boolean> pred) {
		for (A a : as)
			if (pred.f(a))
				return true;
		return false;
	}

	static <A> boolean all(ArrayList<A> as, F2<A, Boolean> pred) {
		for (A a : as)
			if (!pred.f(a))
				return false;
		return true;
	}

	static <A> ArrayList<A> flatten(ArrayList<ArrayList<A>> ass) {
		ArrayList<A> res = new ArrayList<A>();
		for (ArrayList<A> as : ass)
			res.addAll(as);
		return res;
	}

	static <A, B> B foldl(ArrayList<A> as, F3<B, A, B> f, B e) {
		B res = e;
		for (A a : as)
			res = f.f(res, a);
		return res;
	}

	static <A, B> B foldr(ArrayList<A> as, F3<A, B, B> f, B e) {
		B res = e;
		for (int i = as.size() - 1; i >= 0; i--)
			res = f.f(as.get(i), res);
		return res;
	}

	static <A> ArrayList<A> reverse(ArrayList<A> as) {
		int size = as.size();
		return make(size, i -> as.get(size - 1 - i));
	}

	static <A> void forEach(ArrayList<A> as, F1V<A> f) {
		for (A a : as)
			f.f(a);
	}

	static <A extends Comparable<A>> UP<TreeMap<A, Integer>, ArrayList<A>> compress(ArrayList<A> as) {
		TreeSet<A> set = new TreeSet<A>(as);
		TreeMap<A, Integer> map = new TreeMap<A, Integer>();
		ArrayList<A> imap = new ArrayList<A>();
		int i = 0;
		for (A a : set) {
			map.put(a, i++);
			imap.add(a);
		}
		return UP.make(map, imap);
	}

	static <A, B> ArrayList<B> map(ArrayList<A> as, F2<A, B> f) {
		return make(as.size(), (i) -> f.f(as.get(i)));
	}

	static <A, B> ArrayList<UP<A, B>> zip(ArrayList<A> as, ArrayList<B> bs) {
		return make(min(as.size(), bs.size()), (i) -> UP.make(as.get(i), bs.get(i)));
	}

	static <A extends Comparable<A>> A min(A a, A b) {
		return a.compareTo(b) < 0 ? a : b;
	}

	static <A extends Comparable<A>> A max(A a, A b) {
		return a.compareTo(b) > 0 ? a : b;
	}

	static <A extends Comparable<A>> A clamp(A a, A min, A max) {
		return a.compareTo(min) < 0 ? min : a.compareTo(max) > 0 ? max : a;
	}

	static <A> A[] doubleSize(A[] as) {
		return Arrays.copyOf(as, as.length << 1);
	}
}

//Priority Queue
@SuppressWarnings("unchecked")
class PQ<A> {
	private int n;
	private Object[] as;
	private HashMap<Integer, Integer> id2pos;
	private int[] pos2id;
	private int id;
	private Comparator<A> comp;

	PQ(Comparator<A> comp) {
		this.comp = comp;
		as = new Object[64];
		id2pos = new HashMap<Integer, Integer>();
		pos2id = new int[64];
		id = 0;
		n = 1;
	}

	int add(A a) {
		int res = addEntry(a);
		fixUp(n - 1);
		return res;
	}

	A pop() {
		int max = n - 1;
		if (max == 0)
			return null;
		if (max == 1) {
			return removeLast();
		}
		swap(1, max);
		A res = removeLast();
		fixDown(1);
		return res;
	}

	void remove(int id) {
		int max = n - 1;
		if (id <= 0 || id > max)
			throw new ArrayIndexOutOfBoundsException(id);
		int k = id2pos.get(id);
		if (k == max) {
			removeLast();
			return;
		}
		swap(k, max);
		removeLast();
		if (!fixDown(k))
			fixUp(k);
	}

	void update(int id, A a) {
		int k = id2pos.get(id);
		if (k <= 0 || k >= n)
			throw new ArrayIndexOutOfBoundsException(k);
		A p = (A) as[k];
		int cmp = comp.compare(a, p);
		as[k] = a;
		if (cmp > 0) {
			fixDown(k);
		} else if (cmp < 0) {
			fixUp(k);
		}
	}

	boolean isEmpty() {
		return n == 1;
	}

	private A removeLast() {
		n--;
		A res = (A) as[n];
		as[n] = null;
		id2pos.remove(pos2id[n]);
		pos2id[n] = 0;
		return res;
	}

	private boolean fixUp(int k) {
		boolean res = false;
		while (k > 1) {
			sanityCheck();
			if (comp.compare((A) as[k], (A) as[k >> 1]) < 0) {
				swap(k, k >> 1);
				k >>= 1;
				res = true;
				continue;
			}
			break;
		}
		return res;
	}

	private boolean fixDown(int k) {
		boolean res = false;
		int numC = 0;
		while ((numC = numChildren(k)) > 0) {
			sanityCheck();
			A a = (A) as[k];
			A l = (A) as[k << 1];
			if (numC == 1) {
				if (comp.compare(a, l) <= 0)
					return res;
				swap(k, k << 1);
				return true;
			}
			A r = (A) as[k << 1 | 1];
			if (comp.compare(a, l) <= 0 && comp.compare(a, r) <= 0)
				return res;
			res = true;
			if (comp.compare(l, r) < 0)
				swap(k, k = k << 1);
			else
				swap(k, k = k << 1 | 1);
		}
		return res;
	}

	private void swap(int i, int j) {
		Object ta = as[i];
		as[i] = as[j];
		as[j] = ta;
		int ii = pos2id[i];
		int ij = pos2id[j];
		int pi = id2pos.get(ii);
		int pj = id2pos.get(ij);
		id2pos.put(ii, pj);
		id2pos.put(ij, pi);
		pos2id[j] = ii;
		pos2id[i] = ij;
		sanityCheck();
	}

	private void sanityCheck() {
		// TODO: naosu
		for (int k = 1; k < n; k++) {
			if (id2pos.get(pos2id[k]) != k) {
				throw new RuntimeException("faltu!? id=" + pos2id[k] + " pos=" + id2pos.get(pos2id[k]) + " " + n);
			}
		}
	}

	private int addEntry(A a) {
		if (n == as.length) {
			as = U.doubleSize(as);
			pos2id = Arrays.copyOf(pos2id, pos2id.length << 1);
		}
		as[n] = a;
		id2pos.put(++id, n);
		pos2id[n] = id;
		n++;
		return id;
	}

	private int numChildren(int k) {
		int s = n;
		k <<= 1;
		if (k >= s)
			return 0;
		if ((k | 1) >= s)
			return 1;
		return 2;
	}

	public String toString() {
		if (n == 1)
			return "[]";
		String s = null;
		for (int i = 1; i < n; i++) {
			A a = (A) as[i];
			if (s == null)
				s = "[" + a;
			else
				s += ", " + a;
		}
		return s + "]";
	}
}

// Graph
@SuppressWarnings("unchecked")
class G<V, E> {
	private int vSize;
	private Object[] vs; // V
	private Object[] esFrom; // HashMap<Integer, E>
	private Object[] esTo; // HashMap<Integer, E>
	private Object[] pool; // UP<Object, Integer>
	private int poolCounter;

	G() {
		vs = new Object[64];
		esFrom = new Object[64];
		esTo = new Object[64];
		pool = new Object[64];
		vSize = 0;
	}

	V getV(int i) {
		return i < 0 || i >= vs.length ? null : (V) vs[i];
	}

	ArrayList<V> getSortedVs() {
		ArrayList<V> res = new ArrayList<V>();
		for (int i = 0; i < vs.length; i++) {
			if (vs[i] != null)
				res.add((V) vs[i]);
		}
		return res;
	}

	void addV(int i, V v) {
		if (getV(i) != null)
			throw new RuntimeException("duplicate vtx: " + i);
		while (vs.length <= i) {
			vs = U.doubleSize(vs);
			esFrom = U.doubleSize(esFrom);
			esTo = U.doubleSize(esTo);
			pool = U.doubleSize(pool);
		}
		vSize = U.max(vSize, i + 1);
		vs[i] = v;
		esFrom[i] = new HashMap<Integer, E>();
		esTo[i] = new HashMap<Integer, E>();
		pool[i] = UP.make(null, 0);
	}

	void setV(int i, V v) {
		if (getV(i) == null)
			throw new RuntimeException("no such vtx: " + i);
		vs[i] = v;
	}

	void addE(int from, int to, E e) {
		((HashMap<Integer, E>) esFrom[from]).put(to, e);
		((HashMap<Integer, E>) esTo[to]).put(from, e);
	}

	void addUE(int i, int j, E e) {
		addE(i, j, e);
		addE(j, i, e);
	}

	<State> void dfs(int firstIdx, State firstS, F5<State, Integer, Integer, E, State> nextState,
			F3V<State, Integer, ArrayList<Integer>> visit) {
		ArrayDeque<UP<Object, Integer>> deque = new ArrayDeque<UP<Object, Integer>>();
		search(firstIdx, firstS, nextState, visit, deque::push, deque::pop, deque::isEmpty);
	}

	<State> void bfs(int firstIdx, State firstS, F5<State, Integer, Integer, E, State> nextState,
			F3V<State, Integer, ArrayList<Integer>> visit) {
		ArrayDeque<UP<Object, Integer>> deque = new ArrayDeque<UP<Object, Integer>>();
		search(firstIdx, firstS, nextState, visit, deque::addLast, deque::pollFirst, deque::isEmpty);
	}

	<A> ArrayList<UP<A, Integer>> dijkstra(int from, F2<E, A> getWeight, F3<A, A, A> add, Comparator<A> comp, A zero,
			A inf) {
		int n = vSize;
		ArrayList<UP<A, Integer>> res = U.make(n, i -> getV(i) == null ? null : UP.make(i == from ? zero : inf, -1));
		PQ<UP<Integer, A>> q = new PQ<UP<Integer, A>>((i, j) -> comp.compare(i.b, j.b));

		int[] qIs = new int[n];
		ArrayList<UP<Integer, A>> ups = new ArrayList<UP<Integer, A>>();
		for (int i = 0; i < n; i++) {
			ups.add(UP.make(i, inf));
		}

		boolean[] fixed = new boolean[n];

		ups.get(from).b = zero;
		qIs[from] = q.add(ups.get(from));

		while (!q.isEmpty()) {
			UP<Integer, A> up = q.pop();
			Integer i = up.a;
			if (fixed[i])
				continue;
			fixed[i] = true;
			A ai = up.b;
			if (ai == inf)
				break;
			for (Entry<Integer, E> je : ((HashMap<Integer, E>) esFrom[i]).entrySet()) {
				Integer j = je.getKey();
				if (fixed[j])
					continue;
				UP<A, Integer> resj = res.get(j);
				A newA = add.f(ai, getWeight.f(je.getValue()));
				if (comp.compare(resj.a, newA) > 0) {
					resj.a = newA;
					resj.b = i;
					UP<Integer, A> upj = ups.get(j);
					upj.b = newA;
					if (qIs[j] == 0)
						qIs[j] = q.add(upj);
					else
						q.update(qIs[j], upj);
				}
			}
		}
		return res;
	}

	private <State> void search(int firstIdx, State firstS, F5<State, Integer, Integer, E, State> nextState,
			F3V<State, Integer, ArrayList<Integer>> visit, F1V<UP<Object, Integer>> push, F1<UP<Object, Integer>> pop,
			F1<Boolean> isEmpty) {
		boolean[] visited = new boolean[vSize];
		ArrayList<Integer> movedTo = new ArrayList<Integer>();
		push.f(UP.make(firstS, firstIdx));
		visited[firstIdx] = true;
		while (!isEmpty.f()) {
			UP<Object, Integer> si = pop.f();
			State s = (State) si.a;
			Integer i = si.b;
			movedTo.clear();
			for (Entry<Integer, E> je : ((HashMap<Integer, E>) esFrom[i]).entrySet()) {
				Integer j = je.getKey();
				if (!visited[j]) {
					E e = je.getValue();
					State ns = nextState.f(s, i, j, e);
					if (ns != null) {
						movedTo.add(j);
						push.f(pick(ns, j));
						visited[j] = true;
					}
				}
			}
			visit.f(s, i, movedTo);
		}
	}

	private UP<Object, Integer> pick(Object o, Integer i) {
		UP<Object, Integer> p = (UP<Object, Integer>) pool[poolCounter];
		poolCounter = (poolCounter + 1) % vSize;
		p.a = o;
		p.b = i;
		return p;
	}
}

public class Main {
	private static void solve() {
		int v = nei();
		int e = nei();
		int r = nei();
		int[][] std = nis2(e, 3);
		G<Integer, Long> g = new G<Integer, Long>();
		for (int i = 0; i < v; i++) {
			g.addV(i, i);
		}
		for (int i = 0; i < e; i++) {
			int s = std[i][0];
			int t = std[i][1];
			long d = std[i][2];
			g.addE(s, t, d);
		}
		for (UP<Long, Integer> p : g.dijkstra(r, w -> w, (a, b) -> a + b, Long::compare, 0l, Long.MAX_VALUE)) {
			out(p.a == Long.MAX_VALUE ? "INF" : p.a);
		}
	}

	// returns (x, y, d) s.t. ax + by = d
	static long[] exgcd(long a, long b) {
		int sa = a < 0 ? -1 : 1;
		int sb = b < 0 ? -1 : 1;
		a *= sa;
		b *= sb;
		long x = 1;
		long y = 0;
		long z = 0;
		long w = 1;
		while (b > 0) {
			long q = a / b;
			long t = z;
			z = x - q * z;
			x = t;
			t = w;
			w = y - q * w;
			y = t;
			t = b;
			b = a - q * b;
			a = t;
		}
		return new long[] { x * sa, y * sb, a };
	}

	static int[] lis(int[] s) {
		int n = s.length;
		int[] dp = new int[n];
		int[] ids = new int[n];
		int[] pids = new int[n];
		dp[0] = s[0];
		int len = 1;
		int lidx = 0;
		for (int i = 1; i < n; i++) {
			int idx = bs(s[i], dp, 0, len);
			dp[idx] = s[i];
			ids[idx] = i;
			if (idx == len) {
				lidx = i;
				len++;
			}
			if (idx > 0)
				pids[i] = ids[idx - 1];
		}
		int[] lis = new int[len];
		lis[len - 1] = s[lidx];
		for (int i = len - 1; i >= 0; i--) {
			lis[i] = s[lidx];
			lidx = pids[lidx];
		}
		return lis;
	}

	static int bs(int a, int[] as, int from, int num) {
		int min = from;
		int max = from + num - 1;
		while (min < max) {
			int mid = min + max >> 1;
			if (as[mid] < a)
				min = mid + 1;
			else if (as[mid] > a)
				max = mid;
			else
				return mid;
		}
		return as[min] < a ? min + 1 : min;
	}

	static int gcd(int x, int y) {
		x = (x ^ x >> 31) - (x >> 31);
		y = (y ^ y >> 31) - (y >> 31);
		if (x < y) {
			x ^= y;
			y ^= x;
			x ^= y;
		}
		int z = x % y;
		if (z == 0)
			return y;
		return gcd(y, z);
	}

	static long gcd(long x, long y) {
		x = (x ^ x >> 63) - (x >> 63);
		y = (y ^ y >> 63) - (y >> 63);
		if (x < y) {
			x ^= y;
			y ^= x;
			x ^= y;
		}
		long z = x % y;
		if (z == 0)
			return y;
		return gcd(y, z);
	}

	static long modinv(long a, long mod) {
		return modpow(a, mod - 2, mod);
	}

	static long modpow(long a, long b, long mod) {
		if (b == 0)
			return 1;
		if ((b & 1) == 0) {
			long sqrt = modpow(a, b >> 1, mod);
			return sqrt * sqrt % mod;
		}
		return a * modpow(a, b - 1, mod) % mod;
	}

	static long fact(long n) {
		if (n <= 1)
			return 1;
		long res = 2;
		for (long i = 3; i <= n; i++) {
			res *= i;
		}
		return res;
	}

	static long modfact(long n, long mod) {
		if (n <= 1)
			return 1 % mod;
		long res = 2;
		for (long i = 3; i <= n; i++) {
			res *= i;
			res %= mod;
		}
		return res % mod;
	}

	// returns facts([0]) and invfacts([1])
	static long[][] enumfacts(int n, long mod) {
		int num = n + 10;
		long[][] res = new long[2][num];
		long[] facts = res[0];
		long[] invfacts = res[1];
		for (int i = 0; i < num; i++) {
			if (i <= 1) {
				facts[i] = 1;
				invfacts[i] = 1;
			} else {
				facts[i] = facts[i - 1] * i % mod;
				invfacts[i] = modinv(facts[i], mod);
			}
		}
		return res;
	}

	static long modcomb(long n, long m, long mod) {
		if (m > n)
			return 0;
		if (m > n - m) {
			m = n - m;
		}
		long numer = 1;
		for (int i = 0; i < m; i++) {
			numer = numer * (n - i) % mod;
		}
		long denom = modfact(m, mod);
		return numer * modinv(denom, mod) % mod;
	}

	static long modcomb(int n, int m, long[] facts, long[] invfacts, long mod) {
		if (m > n)
			return 0;
		long numer = facts[n];
		long denom = invfacts[m] * invfacts[n - m] % mod;
		return numer * denom % mod;
	}

	// res[i][0]: prime factor, res[i][1]: exponent
	static int[][] factorize(int n) {
		int[][] pfs = new int[32][2];
		int num = 0;
		for (int i = 2; i * i <= n; i++) {
			int count = 0;
			while (n % i == 0) {
				n /= i;
				count++;
			}
			if (count > 0) {
				pfs[num][0] = i;
				pfs[num][1] = count;
				num++;
			}
		}
		if (n > 1) {
			pfs[num][0] = n;
			pfs[num][1] = 1;
			num++;
		}
		int[][] res = new int[num][2];
		for (int i = 0; i < num; i++) {
			res[i][0] = pfs[i][0];
			res[i][1] = pfs[i][1];
		}
		return res;
	}

	static long lcm(long x, long y) {
		x = (x ^ x >> 63) - (x >> 63);
		y = (y ^ y >> 63) - (y >> 63);
		return x / gcd(x, y) * y;
	}

	static int abs(int x) {
		return x < 0 ? -x : x;
	}

	static long abs(long x) {
		return x < 0 ? -x : x;
	}

	static int min(int a, int b) {
		return a < b ? a : b;
	}

	static long min(long a, long b) {
		return a < b ? a : b;
	}

	static int max(int a, int b) {
		return a > b ? a : b;
	}

	static long max(long a, long b) {
		return a > b ? a : b;
	}

	static int clamp(int a, int min, int max) {
		return a < min ? min : a > max ? max : a;
	}

	static long clamp(long a, long min, long max) {
		return a < min ? min : a > max ? max : a;
	}

	static double clamp(double a, double min, double max) {
		return a < min ? min : a > max ? max : a;
	}

	static void out(String val) {
		IO.out(val);
	}

	static void out(Object val) {
		IO.out(String.valueOf(val));
	}

	static void out(int val) {
		IO.out(String.valueOf(val));
	}

	static void out(long val) {
		IO.out(String.valueOf(val));
	}

	static void out(char val) {
		IO.out(String.valueOf(val));
	}

	static void out(double val) {
		IO.out(Double.isFinite(val) ? BigDecimal.valueOf(val).toPlainString() : String.valueOf(val));
	}

	static void out(boolean val) {
		IO.out(val ? "true" : "false");
	}

	static void kil(String val) {
		IO.out(val);
		IO.flush();
		System.exit(0);
	}

	static void kil(Object val) {
		IO.out(String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(int val) {
		IO.out(String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(long val) {
		IO.out(String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(char val) {
		IO.out(String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(double val) {
		IO.out(Double.isFinite(val) ? BigDecimal.valueOf(val).toPlainString() : String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(boolean val) {
		IO.out(val ? "true" : "false");
		IO.flush();
		System.exit(0);
	}

	static String nes() {
		return IO.next();
	}

	static int nei() {
		return IO.nextInt();
	}

	static long nel() {
		return IO.nextLong();
	}

	static double ned() {
		return IO.nextDouble();
	}

	static char nec() {
		return IO.nextChar();
	}

	static String[] nss(int n) {
		String[] as = new String[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.next();
		}
		return as;
	}

	static int[] nis(int n) {
		int[] as = new int[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.nextInt();
		}
		return as;
	}

	static long[] nls(int n) {
		long[] as = new long[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.nextLong();
		}
		return as;
	}

	static double[] nds(int n) {
		double[] as = new double[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.nextDouble();
		}
		return as;
	}

	static char[] ncs(int n) {
		char[] as = new char[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.nextChar();
		}
		return as;
	}

	static String[][] nss2(int n, int m) {
		String[][] as = new String[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.next();
			}
		}
		return as;
	}

	static int[][] nis2(int n, int m) {
		int[][] as = new int[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.nextInt();
			}
		}
		return as;
	}

	static long[][] nls2(int n, int m) {
		long[][] as = new long[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.nextLong();
			}
		}
		return as;
	}

	static double[][] nds2(int n, int m) {
		double[][] as = new double[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.nextDouble();
			}
		}
		return as;
	}

	static char[][] ncs2(int n, int m) {
		char[][] as = new char[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.nextChar();
			}
		}
		return as;
	}

	static int parseInt(String val) {
		return Integer.parseInt(val);
	}

	static int parseInt(char val) {
		return Integer.parseInt(String.valueOf(val));
	}

	static long parseLong(String val) {
		return Long.parseLong(val);
	}

	public static void main(String[] args) {
		try {
			solve();
			IO.flush();
		} catch (NumberFormatException e) {
			e.printStackTrace();
		}
	}
}

final class IO {
	private static final InputStream in = System.in;
	private static final PrintWriter out = new PrintWriter(System.out, false);
	private static final byte[] buffer = new byte[1024];
	private static int ptr = 0;
	private static int len = 0;

	private static boolean hasNextByte() {
		if (ptr < len)
			return true;
		ptr = 0;
		try {
			len = in.read(buffer);
		} catch (IOException e) {
			e.printStackTrace();
		}
		return len > 0;
	}

	private static int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	static boolean hasNext() {
		byte c;
		while (hasNextByte() && ((c = buffer[ptr]) < '!' || c > '~'))
			ptr++;
		return hasNextByte();
	}

	static String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (b >= '!' && b <= '~') {
			sb.append((char) b);
			b = readByte();
		}
		return sb.toString();
	}

	static char nextChar() {
		if (!hasNext())
			throw new NoSuchElementException();
		return (char) readByte();
	}

	static long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		int sign = 1;
		int b = readByte();
		if (b == '-') {
			sign = -1;
			b = readByte();
		}
		if (b < '0' || '9' < b)
			throw new NumberFormatException();
		while (true) {
			if ('0' <= b && b <= '9')
				n = n * 10 + b - '0';
			else if (b == -1 || b < '!' || b > '~')
				return n * sign;
			else
				throw new NumberFormatException();
			b = readByte();
		}
	}

	static int nextInt() {
		if (!hasNext())
			throw new NoSuchElementException();
		int n = 0;
		int sign = 1;
		int b = readByte();
		if (b == '-') {
			sign = -1;
			b = readByte();
		}
		if (b < '0' || '9' < b)
			throw new NumberFormatException();
		while (true) {
			if ('0' <= b && b <= '9')
				n = n * 10 + b - '0';
			else if (b == -1 || b < '!' || b > '~')
				return n * sign;
			else
				throw new NumberFormatException();
			b = readByte();
		}
	}

	static double nextDouble() {
		return Double.parseDouble(next());
	}

	static void out(String val) {
		out.println(val);
	}

	static void flush() {
		out.flush();
	}
}