{"raw_statement":[{"iden":"problem statement","content":"Takahashi is an expert of Clone Jutsu, a secret art that creates copies of his body.\nOn a number line, there are $N$ copies of Takahashi, numbered $1$ through $N$. The $i$\\-th copy is located at position $X_i$ and starts walking with velocity $V_i$ in the positive direction at time $0$.\nKenus is a master of Transformation Jutsu, and not only can he change into a person other than himself, but he can also transform another person into someone else.\nKenus can select some of the copies of Takahashi at time $0$, and transform them into copies of Aoki, another Ninja. The walking velocity of a copy does not change when it transforms. From then on, whenever a copy of Takahashi and a copy of Aoki are at the same coordinate, that copy of Takahashi transforms into a copy of Aoki.\nAmong the $2^N$ ways to transform some copies of Takahashi into copies of Aoki at time $0$, in how many ways will all the copies of Takahashi become copies of Aoki after a sufficiently long time? Find the count modulo $10^9+7$."},{"iden":"constraints","content":"*   $1 ≤ N ≤ 200000$\n*   $1 ≤ X_i,V_i ≤ 10^9(1 ≤ i ≤ N)$\n*   $X_i$ and $V_i$ are integers.\n*   All $X_i$ are distinct.\n*   All $V_i$ are distinct."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$\n$X_1$ $V_1$\n:\n$X_N$ $V_N$"},{"iden":"sample input 1","content":"3\n2 5\n6 1\n3 7"},{"iden":"sample output 1","content":"6\n\nAll copies of Takahashi will turn into copies of Aoki after a sufficiently long time if Kenus transforms one of the following sets of copies of Takahashi into copies of Aoki: $(2)$, $(3)$, $(1,2)$, $(1,3)$, $(2,3)$ and $(1,2,3)$."},{"iden":"sample input 2","content":"4\n3 7\n2 9\n8 16\n10 8"},{"iden":"sample output 2","content":"9"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}