{"problem":{"name":"Traveling","description":{"content":"AtCoDeer the deer is going on a trip in a two-dimensional plane. In his plan, he will depart from point $(0, 0)$ at time $0$, then for each $i$ between $1$ and $N$ (inclusive), he will visit point $(x","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc089_a"},"statements":[{"statement_type":"Markdown","content":"AtCoDeer the deer is going on a trip in a two-dimensional plane. In his plan, he will depart from point $(0, 0)$ at time $0$, then for each $i$ between $1$ and $N$ (inclusive), he will visit point $(x_i,y_i)$ at time $t_i$.\nIf AtCoDeer is at point $(x, y)$ at time $t$, he can be at one of the following points at time $t+1$: $(x+1,y)$, $(x-1,y)$, $(x,y+1)$ and $(x,y-1)$. Note that **he cannot stay at his place**. Determine whether he can carry out his plan.\n\n## Constraints\n\n*   $1$ $≤$ $N$ $≤$ $10^5$\n*   $0$ $≤$ $x_i$ $≤$ $10^5$\n*   $0$ $≤$ $y_i$ $≤$ $10^5$\n*   $1$ $≤$ $t_i$ $≤$ $10^5$\n*   $t_i$ $<$ $t_{i+1}$ ($1$ $≤$ $i$ $≤$ $N-1$)\n*   All input values are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$t_1$ $x_1$ $y_1$\n$t_2$ $x_2$ $y_2$\n$:$\n$t_N$ $x_N$ $y_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc089_a","tags":[],"sample_group":[["2\n3 1 2\n6 1 1","Yes\n\nFor example, he can travel as follows: $(0,0)$, $(0,1)$, $(1,1)$, $(1,2)$, $(1,1)$, $(1,0)$, then $(1,1)$."],["1\n2 100 100","No\n\nIt is impossible to be at $(100,100)$ two seconds after being at $(0,0)$."],["2\n5 1 1\n100 1 1","No"]],"created_at":"2026-03-03 11:01:13"}}