{"raw_statement":[{"iden":"problem statement","content":"There are $N$ people standing on the $x$\\-axis. Let the coordinate of Person $i$ be $x_i$. For every $i$, $x_i$ is an integer between $0$ and $10^9$ (inclusive). It is possible that more than one person is standing at the same coordinate.\nYou will given $M$ pieces of information regarding the positions of these people. The $i$\\-th piece of information has the form $(L_i, R_i, D_i)$. This means that Person $R_i$ is to the right of Person $L_i$ by $D_i$ units of distance, that is, $x_{R_i} - x_{L_i} = D_i$ holds.\nIt turns out that some of these $M$ pieces of information may be incorrect. Determine if there exists a set of values $(x_1, x_2, ..., x_N)$ that is consistent with the given pieces of information."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 100$ $000$\n*   $0 \\leq M \\leq 200$ $000$\n*   $1 \\leq L_i, R_i \\leq N$ ($1 \\leq i \\leq M$)\n*   $0 \\leq D_i \\leq 10$ $000$ ($1 \\leq i \\leq M$)\n*   $L_i \\neq R_i$ ($1 \\leq i \\leq M$)\n*   If $i \\neq j$, then $(L_i, R_i) \\neq (L_j, R_j)$ and $(L_i, R_i) \\neq (R_j, L_j)$.\n*   $D_i$ are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$\n$L_1$ $R_1$ $D_1$\n$L_2$ $R_2$ $D_2$\n$:$\n$L_M$ $R_M$ $D_M$"},{"iden":"sample input 1","content":"3 3\n1 2 1\n2 3 1\n1 3 2"},{"iden":"sample output 1","content":"Yes\n\nSome possible sets of values $(x_1, x_2, x_3)$ are $(0, 1, 2)$ and $(101, 102, 103)$."},{"iden":"sample input 2","content":"3 3\n1 2 1\n2 3 1\n1 3 5"},{"iden":"sample output 2","content":"No\n\nIf the first two pieces of information are correct, $x_3 - x_1 = 2$ holds, which is contradictory to the last piece of information."},{"iden":"sample input 3","content":"4 3\n2 1 1\n2 3 5\n3 4 2"},{"iden":"sample output 3","content":"Yes"},{"iden":"sample input 4","content":"10 3\n8 7 100\n7 9 100\n9 8 100"},{"iden":"sample output 4","content":"No"},{"iden":"sample input 5","content":"100 0"},{"iden":"sample output 5","content":"Yes"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}