Problem: 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).

Constraints

* 1 ≤ |V| ≤ 100000
* 0 ≤ di ≤ 10000
* 0 ≤ |E| ≤ 500000
* There are no parallel edges
* There are no self-loops

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.

Examples

Input

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


Output

0
1
3
4


Input

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


Output

3
0
2
INF

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

using namespace std;

using ll = long long;
constexpr ll MOD = 1e9 + 7;
constexpr ll INF = 1e18;

int a[]={1,-1,5,-5,10,-10};

int main() {
    ll V,E,r;
    cin >> V >> E >> r;
    vector<vector<pair<ll,ll>>> G(V);
    for(ll i=0;i<E;i++){
        ll x,y,cost;
        cin >> x >> y >> cost;
        G[x].push_back({y,cost});
    }
    vector<ll> dist(V,INF),used(V,0);
    dist[r]=0;
    priority_queue<pair<ll,ll>,vector<pair<ll,ll>>,greater<pair<ll,ll>>> pq;
    pq.push({0,r});
    while(!pq.empty()){
        ll pos,d;
        pos = pq.top().second;
        d = pq.top().first;
        pq.pop();
        if(used[pos]==1)continue;
        used[pos]=1;
        for(auto &x:G[pos]){
            if(dist[x.first]>d+x.second){
                dist[x.first] = d+x.second;
                pq.push({dist[x.first],x.first});
            }
        }
    }
    for(auto &x:dist){
        if(x!=INF)cout << x << endl;
        else cout << "INF" << endl;
    }
}