Range Connect MST

AtCoder

IDabc364_f

Time2000ms

Memory256MB

Difficulty—

There is a graph with $N + Q$ vertices, numbered $1, 2, \ldots, N + Q$. Initially, the graph has no edges. For this graph, perform the following operation for $i = 1, 2, \ldots, Q$ in order: * For each integer $j$ satisfying $L_i \leq j \leq R_i$, add an undirected edge with cost $C_i$ between vertices $N + i$ and $j$. Determine if the graph is connected after all operations are completed. If it is connected, find the cost of a minimum spanning tree of the graph. A minimum spanning tree is a spanning tree with the smallest possible cost, and the cost of a spanning tree is the sum of the costs of the edges used in the spanning tree. ## Constraints * $1 \leq N, Q \leq 2 \times 10^5$ * $1 \leq L_i \leq R_i \leq N$ * $1 \leq C_i \leq 10^9$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $Q$ $L_1$ $R_1$ $C_1$ $L_2$ $R_2$ $C_2$ $\vdots$ $L_Q$ $R_Q$ $C_Q$ [samples]

Samples

Input #1

Output #1

22

The following edges form a minimum spanning tree:

*   An edge with cost $2$ connecting vertices $1$ and $5$
*   An edge with cost $2$ connecting vertices $2$ and $5$
*   An edge with cost $4$ connecting vertices $1$ and $6$
*   An edge with cost $4$ connecting vertices $3$ and $6$
*   An edge with cost $5$ connecting vertices $3$ and $7$
*   An edge with cost $5$ connecting vertices $4$ and $7$

Since $2 + 2 + 4 + 4 + 5 + 5 = 22$, print $22$.

Input #2

6 2
1 2 10
4 6 10

Output #2

\-1

The graph is disconnected.

Input #3

200000 4
1 200000 1000000000
1 200000 998244353
1 200000 999999999
1 200000 999999999

Output #3

199651870599998

API Response (JSON)

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