use std::io::{Write, BufWriter}; // https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes.by_ref().map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr,) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, ( $($t:tt),* )) => { ($(read_value!($next, $t)),*) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, [ $t:tt ]) => {{ let len = read_value!($next, usize); read_value!($next, [$t; len]) }}; ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } /// Verified by https://atcoder.jp/contests/abc198/submissions/21774342 mod mod_int { use std::ops::*; pub trait Mod: Copy { fn m() -> i64; } #[derive(Copy, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)] pub struct ModInt { pub x: i64, phantom: ::std::marker::PhantomData } impl ModInt { // x >= 0 pub fn new(x: i64) -> Self { ModInt::new_internal(x % M::m()) } fn new_internal(x: i64) -> Self { ModInt { x: x, phantom: ::std::marker::PhantomData } } pub fn pow(self, mut e: i64) -> Self { debug_assert!(e >= 0); let mut sum = ModInt::new_internal(1); let mut cur = self; while e > 0 { if e % 2 != 0 { sum *= cur; } cur *= cur; e /= 2; } sum } #[allow(dead_code)] pub fn inv(self) -> Self { self.pow(M::m() - 2) } } impl Default for ModInt { fn default() -> Self { Self::new_internal(0) } } impl>> Add for ModInt { type Output = Self; fn add(self, other: T) -> Self { let other = other.into(); let mut sum = self.x + other.x; if sum >= M::m() { sum -= M::m(); } ModInt::new_internal(sum) } } impl>> Sub for ModInt { type Output = Self; fn sub(self, other: T) -> Self { let other = other.into(); let mut sum = self.x - other.x; if sum < 0 { sum += M::m(); } ModInt::new_internal(sum) } } impl>> Mul for ModInt { type Output = Self; fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) } } impl>> AddAssign for ModInt { fn add_assign(&mut self, other: T) { *self = *self + other; } } impl>> SubAssign for ModInt { fn sub_assign(&mut self, other: T) { *self = *self - other; } } impl>> MulAssign for ModInt { fn mul_assign(&mut self, other: T) { *self = *self * other; } } impl Neg for ModInt { type Output = Self; fn neg(self) -> Self { ModInt::new(0) - self } } impl ::std::fmt::Display for ModInt { fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result { self.x.fmt(f) } } impl From for ModInt { fn from(x: i64) -> Self { Self::new(x) } } } // mod mod_int macro_rules! define_mod { ($struct_name: ident, $modulo: expr) => { #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)] struct $struct_name {} impl mod_int::Mod for $struct_name { fn m() -> i64 { $modulo } } } } const MOD: i64 = 998_244_353; define_mod!(P, MOD); type MInt = mod_int::ModInt

; // https://yukicoder.me/problems/no/2310 (3.5) // dp[i][j]: 元のグラフにおける i から j へのパスの総数 とすると、これは O(N^3)-time で計算できる。 // クエリに対しては、ep[i][1] := クエリで与えられた辺を最後に使う 0 から i へのパスの総数 とすると、 // これは O(K^2)-time で計算できる。合計 O(N^3 + QK^2)-time。 fn main() { let out = std::io::stdout(); let mut out = BufWriter::new(out.lock()); macro_rules! puts {($($format:tt)*) => (let _ = write!(out,$($format)*););} input! { n: usize, x: [[i64; n + 1]; n + 1], q: usize, abc: [[(usize, usize, i64)]; q], } let mut dp = vec![vec![MInt::new(0); n + 1]; n + 1]; for i in 0..n + 1 { dp[i][i] += 1; } for s in 1..n + 1 { for i in 0..n + 1 - s { let j = i + s; let mut me = MInt::new(0); for k in i..j { me += dp[i][k] * x[k][j]; } dp[i][j] = me; } } for abc in abc { let mut coo = vec![]; for &(a, b, _) in &abc { coo.push(a); coo.push(b); } coo.sort(); coo.dedup(); let m = coo.len(); let mut ep = vec![[MInt::new(0); 2]; m]; let mut g = vec![vec![]; m]; for &(a, b, c) in &abc { let a = coo.binary_search(&a).unwrap(); let b = coo.binary_search(&b).unwrap(); g[b].push((a, MInt::new(c))); } for i in 0..m { ep[i][0] += dp[0][coo[i]]; for &(from, mul) in &g[i] { ep[i][1] = ep[i][1] + ep[from][0] * mul; } for j in 0..i + 1 { let from = coo[j]; ep[i][0] = ep[i][0] + ep[j][1] * dp[from][coo[i]]; } } let mut tot = dp[0][n]; for i in 0..m { tot += ep[i][1] * dp[coo[i]][n]; } puts!("{}\n", tot); } }