{"raw_statement":[{"iden":"problem statement","content":"You are given a sequence $(A_1, A_2, \\ldots , A_N)$. Let us define a sequence $(F_0, F_1, \\ldots , F_N)$ by the following formulae.\n\n*   $F_0 = 1$\n*   $F_n = A_n\\displaystyle\\sum_{i+j<n}F_iF_j$ $(1 \\leq n \\leq N)$\n\nFind $F_1, \\ldots , F_N$ modulo $998244353$."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $0 \\leq A_i < 998244353$\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ $\\ldots$ $A_N$"},{"iden":"sample input 1","content":"5\n1 2 3 4 5"},{"iden":"sample output 1","content":"1 6 48 496 6240\n\n$F_1 = A_1F_0F_0 = 1$. $F_2 = A_2(F_0F_0+F_0F_1+F_1F_0) = 6$. Similarly, we find $F_3 = 48, F_4 = 496, F_5 = 6240$."},{"iden":"sample input 2","content":"3\n12345 678901 2345678"},{"iden":"sample output 2","content":"12345 790834943 85679169"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}