2 - Shortest Path on a Line

We have N points numbered 1 to N arranged in a line in this order.

Takahashi decides to make an undirected graph, using these points as the vertices. In the beginning, the graph has no edge. Takahashi will do M operations to add edges in this graph. The i-th operation is as follows:

• The operation uses integers L_i and R_i between 1 and N (inclusive), and a positive integer C_i. For every pair of integers (s, t) such that L_i \leq s < t \leq R_i, add an edge of length C_i between Vertex s and Vertex t.

The integers L_1, ..., L_M, R_1, ..., R_M, C_1, ..., C_M are all given as input.

Takahashi wants to solve the shortest path problem in the final graph obtained. Find the length of the shortest path from Vertex 1 to Vertex N in the final graph.

Constraints

• 2 \leq N \leq 10^5
• 1 \leq M \leq 10^5
• 1 \leq L_i < R_i \leq N
• 1 \leq C_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N M L_1 R_1 C_1 : L_M R_M C_M

Output

Print the length of the shortest path from Vertex 1 to Vertex N in the final graph. If there is no shortest path, print -1 instead.

Examples

Input

4 3 1 3 2 2 4 3 1 4 6

Output

5

Input

4 2 1 2 1 3 4 2

Output

-1

Input

10 7 1 5 18 3 4 8 1 3 5 4 7 10 5 9 8 6 10 5 8 10 3

Output

28

inputFormat

input.

Takahashi wants to solve the shortest path problem in the final graph obtained. Find the length of the shortest path from Vertex 1 to Vertex N in the final graph.

Constraints

• 2 \leq N \leq 10^5
• 1 \leq M \leq 10^5
• 1 \leq L_i < R_i \leq N
• 1 \leq C_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N M L_1 R_1 C_1 : L_M R_M C_M

outputFormat

Output

Print the length of the shortest path from Vertex 1 to Vertex N in the final graph. If there is no shortest path, print -1 instead.

Examples

Input

4 3 1 3 2 2 4 3 1 4 6

Output

5

Input

4 2 1 2 1 3 4 2

Output

-1

Input

10 7 1 5 18 3 4 8 1 3 5 4 7 10 5 9 8 6 10 5 8 10 3

Output

28

样例

4 3
1 3 2
2 4 3
1 4 6

5