use mod_int::ModInt1000000007; pub mod utils { const DYX: [(isize, isize); 8] = [ (0, 1), (1, 0), (0, -1), (-1, 0), (1, 1), (-1, 1), (1, -1), (-1, -1), ]; pub fn try_adj(y: usize, x: usize, dir: usize, h: usize, w: usize) -> Option<(usize, usize)> { let ny = y as isize + DYX[dir].0; let nx = x as isize + DYX[dir].1; if ny >= 0 && nx >= 0 && ny < h as isize && nx < w as isize { Some((ny as usize, nx as usize)) } else { None } } } /// Modular Integer /// NOTE /// If a modular isn't prime, you can't div. /// If you want to calculate a combination and permutation, you have to use `mod_comb`. pub mod mod_int { use std::marker::PhantomData; use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Sub, SubAssign}; #[derive(Copy, Clone, Ord, PartialOrd, Eq, PartialEq, Hash, Debug)] pub struct Mod1000000007; #[derive(Copy, Clone, Ord, PartialOrd, Eq, PartialEq, Hash, Debug)] pub struct Mod998244353; pub trait Modulus: Copy + Eq + Copy { const VALUE: u32; } impl Modulus for Mod1000000007 { const VALUE: u32 = 1000000007; } impl Modulus for Mod998244353 { const VALUE: u32 = 998244353; } #[derive(Clone, Copy, Debug, PartialEq, Eq)] pub struct ModInt< T: Copy + Clone + Add + AddAssign + Mul + MulAssign + Sub + SubAssign, M: Modulus, > { pub val: T, phantom: std::marker::PhantomData M>, } /// Implementation macros #[warn(unused_macros)] macro_rules ! mod_int_impl {($ ($ t : ty ) * ) => ($ (impl < M : Modulus > ModInt <$ t , M > {pub fn new (x : $ t ) -> Self {ModInt {val : x % M :: VALUE as $ t , phantom : PhantomData } } pub fn pow (self , e : usize ) -> ModInt <$ t , M > {let mut result = ModInt ::<$ t , M >:: new (1 ) ; let mut cur = self ; let mut e = e ; while e > 0 {if e & 1 == 1 {result *= cur ; } cur *= cur ; e >>= 1 ; } result } } impl < M : Modulus > Add < ModInt <$ t , M >> for ModInt <$ t , M > {type Output = ModInt <$ t , M >; fn add (self , rhs : ModInt <$ t , M > ) -> ModInt <$ t , M > {self + rhs . val } } impl < M : Modulus > Add < ModInt <$ t , M >> for $ t {type Output = ModInt <$ t , M >; fn add (self , rhs : ModInt <$ t , M > ) -> ModInt <$ t , M > {let x = self % M :: VALUE as $ t ; let val = (x + rhs . val ) % M :: VALUE as $ t ; ModInt {val , phantom : PhantomData } } } impl < M : Modulus > Add <$ t > for ModInt <$ t , M > {type Output = ModInt <$ t , M >; fn add (self , rhs : $ t ) -> ModInt <$ t , M > {let x = rhs % M :: VALUE as $ t ; let val = (self . val + x ) % M :: VALUE as $ t ; ModInt {val , phantom : PhantomData } } } impl < M : Modulus > Sub < ModInt <$ t , M >> for ModInt <$ t , M > {type Output = ModInt <$ t , M >; fn sub (self , rhs : ModInt <$ t , M > ) -> ModInt <$ t , M > {self - rhs . val } } impl < M : Modulus > Sub < ModInt <$ t , M >> for $ t {type Output = ModInt <$ t , M >; fn sub (self , rhs : ModInt <$ t , M > ) -> ModInt <$ t , M > {let val = self % M :: VALUE as $ t ; ModInt {val , phantom : PhantomData } - rhs } } impl < M : Modulus > Sub <$ t > for ModInt <$ t , M > {type Output = ModInt <$ t , M >; fn sub (self , rhs : $ t ) -> ModInt <$ t , M > {let rhs = if rhs >= M :: VALUE as $ t {rhs % M :: VALUE as $ t } else {rhs } ; let val = if self . val < rhs {self . val + M :: VALUE as $ t - rhs } else {self . val - rhs } ; ModInt {val , phantom : PhantomData } } } impl < M : Modulus > AddAssign < ModInt <$ t , M >> for ModInt <$ t , M > {fn add_assign (& mut self , rhs : ModInt <$ t , M > ) {* self = * self + rhs ; } } impl < M : Modulus > AddAssign <$ t > for ModInt <$ t , M > {fn add_assign (& mut self , rhs : $ t ) {* self = * self + rhs ; } } impl < M : Modulus > SubAssign < ModInt <$ t , M >> for ModInt <$ t , M > {fn sub_assign (& mut self , rhs : ModInt <$ t , M > ) {* self = * self - rhs ; } } impl < M : Modulus > SubAssign <$ t > for ModInt <$ t , M > {fn sub_assign (& mut self , rhs : $ t ) {* self = * self - rhs ; } } impl < M : Modulus > Div <$ t > for ModInt <$ t , M > {type Output = ModInt <$ t , M >; fn div (self , mut rhs : $ t ) -> ModInt <$ t , M > {if rhs >= M :: VALUE as $ t {rhs %= M :: VALUE as $ t ; } self * ModInt {val : rhs , phantom : PhantomData } . pow ((M :: VALUE - 2 ) as usize ) } } impl < M : Modulus > Div < ModInt <$ t , M >> for ModInt <$ t , M > {type Output = ModInt <$ t , M >; fn div (self , rhs : ModInt <$ t , M > ) -> ModInt <$ t , M > {self / rhs . val } } impl < M : Modulus > DivAssign <$ t > for ModInt <$ t , M > {fn div_assign (& mut self , rhs : $ t ) {* self = * self / rhs } } impl < M : Modulus > DivAssign < ModInt <$ t , M >> for ModInt <$ t , M > {fn div_assign (& mut self , rhs : ModInt <$ t , M > ) {* self = * self / rhs } } impl < M : Modulus > Mul < ModInt <$ t , M >> for ModInt <$ t , M > {type Output = ModInt <$ t , M >; fn mul (self , rhs : ModInt <$ t , M > ) -> ModInt <$ t , M > {self * rhs . val } } impl < M : Modulus > Mul < ModInt <$ t , M >> for $ t {type Output = ModInt <$ t , M >; fn mul (self , rhs : ModInt <$ t , M > ) -> ModInt <$ t , M > {rhs * self } } impl < M : Modulus > Mul <$ t > for ModInt <$ t , M > {type Output = ModInt <$ t , M >; fn mul (self , rhs : $ t ) -> ModInt <$ t , M > {ModInt {val : self . val * (rhs % M :: VALUE as $ t ) % M :: VALUE as $ t , phantom : PhantomData } } } impl < M : Modulus > MulAssign < ModInt <$ t , M >> for ModInt <$ t , M > {fn mul_assign (& mut self , rhs : ModInt <$ t , M > ) {* self = * self * rhs ; } } impl < M : Modulus > MulAssign <$ t > for ModInt <$ t , M > {fn mul_assign (& mut self , rhs : $ t ) {* self = * self * rhs ; } } impl < M : Modulus > Default for ModInt <$ t , M > {fn default () -> ModInt <$ t , M > {ModInt {val : 0 , phantom : PhantomData } } } ) * ) } mod_int_impl ! (usize i64 u64 i128 ); #[allow(dead_code)] pub type ModInt1000000007 = ModInt; pub type ModInt998244353 = ModInt; } #[derive(Default)] /// NOTE /// declare variables to reduce the number of parameters for dp and dfs etc. pub struct Solver {} impl Solver { pub fn solve(&mut self) { let stdin = std::io::stdin(); let mut scn = fastio::Scanner::new(stdin.lock()); let n: usize = scn.read(); let a = scn.vec::(n); let mut result = ModInt1000000007::new(0); let mut cross= ModInt1000000007::new(1); for i in 0..n-1 { cross *= a[i]; let r2 = cross * ModInt1000000007::new(3).pow(n-2-i) * 2; result += r2; } result += cross*a[n-1]; println!("{}", result.val); } } pub mod fastio { use std::collections::VecDeque; use std::io::BufWriter; use std::io::Write; pub struct Writer { writer: std::io::BufWriter, } impl Writer { pub fn new(write: W) -> Writer { Writer { writer: BufWriter::new(write), } } pub fn flush(&mut self) { self.writer.flush().unwrap(); } pub fn write(&mut self, s: S) { self.writer.write(s.to_string().as_bytes()).unwrap(); } pub fn writeln(&mut self, s: S) { self.write(s); self.write('\n'); } } pub struct Scanner { stdin: R, buffer: VecDeque, } impl Scanner { pub fn new(s: R) -> Scanner { Scanner { stdin: s, buffer: VecDeque::new(), } } pub fn read(&mut self) -> T { while self.buffer.is_empty() { let line = self.read_line(); for w in line.split_whitespace() { self.buffer.push_back(String::from(w)); } } self.buffer.pop_front().unwrap().parse::().ok().unwrap() } pub fn read_line(&mut self) -> String { let mut line = String::new(); let _ = self.stdin.read_line(&mut line); line.trim_end().to_string() } pub fn vec(&mut self, n: usize) -> Vec { (0..n).map(|_| self.read()).collect() } pub fn chars(&mut self) -> Vec { self.read::().chars().collect() } } } pub mod macros { #[macro_export] #[allow(unused_macros)] macro_rules ! max {($ x : expr ) => ($ x ) ; ($ x : expr , $ ($ y : expr ) ,+ ) => {std :: cmp :: max ($ x , max ! ($ ($ y ) ,+ ) ) } } #[macro_export] #[allow(unused_macros)] macro_rules ! min {($ x : expr ) => ($ x ) ; ($ x : expr , $ ($ y : expr ) ,+ ) => {std :: cmp :: min ($ x , min ! ($ ($ y ) ,+ ) ) } } #[macro_export] #[allow(unused_macros)] /// Display a line of variables macro_rules ! echo {() => {{use std :: io :: {self , Write } ; writeln ! (io :: stderr () , "{}:" , line ! () ) . unwrap () ; } } ; ($ e : expr , $ ($ es : expr ) ,+ $ (, ) ? ) => {{use std :: io :: {self , Write } ; write ! (io :: stderr () , "{}:" , line ! () ) . unwrap () ; write ! (io :: stderr () , " {} = {:?}" , stringify ! ($ e ) , $ e ) . unwrap () ; $ (write ! (io :: stderr () , " {} = {:?}" , stringify ! ($ es ) , $ es ) . unwrap () ; ) + writeln ! (io :: stderr () ) . unwrap () ; } } ; ($ e : expr ) => {{use std :: io :: {self , Write } ; let result = $ e ; writeln ! (io :: stderr () , "{}: {} = {:?}" , line ! () , stringify ! ($ e ) , result ) . unwrap () ; result } } ; } #[macro_export] #[allow(unused_macros)] /// Display a line of variables with colors macro_rules ! cecho {() => {{use std :: io :: {self , Write } ; writeln ! (io :: stderr () , "\x1b[31;1m{}\x1b[m:" , line ! () ) . unwrap () ; } } ; ($ e : expr , $ ($ es : expr ) ,+ $ (, ) ? ) => {{use std :: io :: {self , Write } ; write ! (io :: stderr () , "\x1b[31;1m{}\x1b[m:" , line ! () ) . unwrap () ; write ! (io :: stderr () , " \x1b[92;1m{}\x1b[m = {:?}" , stringify ! ($ e ) , $ e ) . unwrap () ; $ (write ! (io :: stderr () , " \x1b[92;1m{}\x1b[m = {:?}" , stringify ! ($ es ) , $ es ) . unwrap () ; ) + writeln ! (io :: stderr () ) . unwrap () ; } } ; ($ e : expr ) => {{use std :: io :: {self , Write } ; let result = $ e ; writeln ! (io :: stderr () , "\x1b[31;1m{}\x1b[m: \x1b[92;1m{}\x1b[m = {:?}" , line ! () , stringify ! ($ e ) , result ) . unwrap () ; result } } ; } } fn main() { std::thread::Builder::new() .stack_size(64 * 1024 * 1024) .spawn(|| Solver::default().solve()) .unwrap() .join() .unwrap(); }