There are n cities and m bidirectional roads in the country. The roads in the country form an undirected weighted graph. The graph is not guaranteed to be connected. Each road has it's own parameter w. You can travel through the roads, but the government made a new law: you can only go through two roads at a time (go from city a to city b and then from city b to city c) and you will have to pay (w_{ab} + w_{bc})^2 money to go through those roads. Find out whether it is possible to travel from city 1 to every other city t and what's the minimum amount of money you need to get from 1 to t.

Input

First line contains two integers n, m (2 ≤ n ≤ 10^5, 1 ≤ m ≤ min((n ⋅ (n - 1))/(2), 2 ⋅ 10^5)).

Next m lines each contain three integers v_i, u_i, w_i (1 ≤ v_i, u_i ≤ n, 1 ≤ w_i ≤ 50, u_i ≠ v_i). It's guaranteed that there are no multiple edges, i.e. for any edge (u_i, v_i) there are no other edges (u_i, v_i) or (v_i, u_i).

Output

For every city t print one integer. If there is no correct path between 1 and t output -1. Otherwise print out the minimum amount of money needed to travel from 1 to t.

Examples

Input


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


Output


0 98 49 25 114 

Input


3 2
1 2 1
2 3 2


Output


0 -1 9 

Note

The graph in the first example looks like this.

<image>

In the second example the path from 1 to 3 goes through 2, so the resulting payment is (1 + 2)^2 = 9.

<image>
import java.io.*;
import java.text.CollationElementIterator;
import java.util.*;

public class Main {

    static final long INF = (long) 1e18;
    static ArrayList<Edge> adjList[];
    static int n;


    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner();
        PrintWriter out = new PrintWriter(System.out);
        n = sc.nextInt();
        int m = sc.nextInt();
        adjList = new ArrayList[n];
        for (int i = 0; i < n; i++)
            adjList[i] = new ArrayList<>();
        while (m-- > 0) {
            int u = sc.nextInt() - 1, v = sc.nextInt() - 1, w = sc.nextInt();
            adjList[u].add(new Edge(v, w));
            adjList[v].add(new Edge(u, w));
        }
        long[] dist = new long[n];
        Arrays.fill(dist, INF);
        PriorityQueue<Edge> pq = new PriorityQueue<>();
        pq.add(new Edge(0, 0));
        dist[0] = 0;
        while (!pq.isEmpty()) {
            Edge cur = pq.remove();
            int u = cur.u;
            long cost = cur.w;
            if (dist[u] < cost) continue;
            for (Edge a : adjList[u])
                for (Edge b : adjList[a.u]) {
                    long next = cost + sq(a.w + b.w);
                    if (next < dist[b.u])
                        pq.add(new Edge(b.u, dist[b.u] = next));
                }
        }
        for (long d : dist)
            if (d == INF)
                out.print(-1 + " ");
            else out.print(d + " ");
        out.flush();
        out.close();
    }

    static long sq(long x) {
        return x * x;
    }

    static class Edge implements Comparable<Edge> {
        int u;
        long w;

        public Edge(int u, long w) {
            this.u = u;
            this.w = w;
        }

        @Override
        public int compareTo(Edge o) {
            return Long.compare(w, o.w);
        }
    }


    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public Scanner(String s) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(s));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public int[] nextIntArray(int n) throws IOException {
            int[] ans = new int[n];
            for (int i = 0; i < n; i++)
                ans[i] = nextInt();
            return ans;
        }

        public long[] nextLongArray(int n) throws IOException {
            long[] ans = new long[n];
            for (int i = 0; i < n; i++)
                ans[i] = nextLong();
            return ans;
        }

        public Integer[] nextIntegerArray(int n) throws IOException {
            Integer[] ans = new Integer[n];
            for (int i = 0; i < n; i++)
                ans[i] = nextInt();
            return ans;
        }

        public char nextChar() throws IOException {
            return next().charAt(0);
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public boolean ready() throws IOException {
            return br.ready();
        }


    }
}