{"raw_statement":[{"iden":"statement","content":"You are given a sequence of positive integers _a_1, _a_2, ..., _a__n_.\n\nWhile possible, you perform the following operation: find a pair of equal consecutive elements. If there are more than one such pair, find the leftmost (with the smallest indices of elements). If the two integers are equal to _x_, delete both and insert a single integer _x_ + 1 on their place. This way the number of elements in the sequence is decreased by 1 on each step.\n\nYou stop performing the operation when there is no pair of equal consecutive elements.\n\nFor example, if the initial sequence is \\[5, 2, 1, 1, 2, 2\\], then after the first operation you get \\[5, 2, 2, 2, 2\\], after the second — \\[5, 3, 2, 2\\], after the third — \\[5, 3, 3\\], and finally after the fourth you get \\[5, 4\\]. After that there are no equal consecutive elements left in the sequence, so you stop the process.\n\nDetermine the final sequence after you stop performing the operation."},{"iden":"input","content":"The first line contains a single integer _n_ (2 ≤ _n_ ≤ 2·105) — the number of elements in the sequence.\n\nThe second line contains the sequence of integers _a_1, _a_2, ..., _a__n_ (1 ≤ _a__i_ ≤ 109)."},{"iden":"output","content":"In the first line print a single integer _k_ — the number of elements in the sequence after you stop performing the operation.\n\nIn the second line print _k_ integers — the sequence after you stop performing the operation."},{"iden":"examples","content":"Input\n\n6\n5 2 1 1 2 2\n\nOutput\n\n2\n5 4 \n\nInput\n\n4\n1000000000 1000000000 1000000000 1000000000\n\nOutput\n\n1\n1000000002 \n\nInput\n\n7\n4 10 22 11 12 5 6\n\nOutput\n\n7\n4 10 22 11 12 5 6"},{"iden":"note","content":"The first example is described in the statements.\n\nIn the second example the initial sequence is \\[1000000000, 1000000000, 1000000000, 1000000000\\]. After the first operation the sequence is equal to \\[1000000001, 1000000000, 1000000000\\]. After the second operation the sequence is \\[1000000001, 1000000001\\]. After the third operation the sequence is \\[1000000002\\].\n\nIn the third example there are no two equal consecutive elements initially, so the sequence does not change."}],"translated_statement":[{"iden":"statement","content":"你被给定一个正整数序列 #cf_span[a1, a2, ..., an]。\n\n在可能的情况下，你执行以下操作：找到一对相等的相邻元素。如果有多个这样的配对，选择最左边的（即元素下标最小的）。如果这两个整数都等于 #cf_span[x]，则将它们删除，并在它们的位置插入一个整数 #cf_span[x + 1]。这样，序列的元素个数在每一步减少 #cf_span[1]。\n\n当序列中不再存在任何相等的相邻元素时，你停止操作。\n\n例如，如果初始序列为 #cf_span[[5, 2, 1, 1, 2, 2]]，则第一次操作后得到 #cf_span[[5, 2, 2, 2, 2]]，第二次操作后得到 #cf_span[[5, 3, 2, 2]]，第三次操作后得到 #cf_span[[5, 3, 3]]，第四次操作后得到 #cf_span[[5, 4]]。此时序列中已无相等的相邻元素，因此停止过程。\n\n请确定在停止操作后得到的最终序列。\n\n第一行包含一个整数 #cf_span[n] (#cf_span[2 ≤ n ≤ 2·105]) —— 序列中元素的个数。\n\n第二行包含整数序列 #cf_span[a1, a2, ..., an] (#cf_span[1 ≤ ai ≤ 109])。\n\n第一行输出一个整数 #cf_span[k] —— 停止操作后序列中元素的个数。\n\n第二行输出 #cf_span[k] 个整数 —— 停止操作后的序列。\n\n第一个例子已在题面中描述。\n\n在第二个例子中，初始序列为 #cf_span[[1000000000, 1000000000, 1000000000, 1000000000]]。第一次操作后序列变为 #cf_span[[1000000001, 1000000000, 1000000000]]。第二次操作后序列变为 #cf_span[[1000000001, 1000000001]]。第三次操作后序列变为 #cf_span[[1000000002]]。\n\n在第三个例子中，初始序列中没有相等的相邻元素，因此序列保持不变。"},{"iden":"input","content":"第一行包含一个整数 #cf_span[n] (#cf_span[2 ≤ n ≤ 2·105]) —— 序列中元素的个数。第二行包含整数序列 #cf_span[a1, a2, ..., an] (#cf_span[1 ≤ ai ≤ 109])。"},{"iden":"output","content":"第一行输出一个整数 #cf_span[k] —— 停止操作后序列中元素的个数。第二行输出 #cf_span[k] 个整数 —— 停止操作后的序列。"},{"iden":"examples","content":"输入65 2 1 1 2 2输出25 4 输入41000000000 1000000000 1000000000 1000000000输出11000000002 输入74 10 22 11 12 5 6输出74 10 22 11 12 5 6 "},{"iden":"note","content":"第一个例子已在题面中描述。在第二个例子中，初始序列为 #cf_span[[1000000000, 1000000000, 1000000000, 1000000000]]。第一次操作后序列变为 #cf_span[[1000000001, 1000000000, 1000000000]]。第二次操作后序列变为 #cf_span[[1000000001, 1000000001]]。第三次操作后序列变为 #cf_span[[1000000002]]。在第三个例子中，初始序列中没有相等的相邻元素，因此序列保持不变。"}],"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ n \\in \\mathbb{Z} $ be the initial length of the sequence.  \nLet $ A = (a_1, a_2, \\dots, a_n) $ be the initial sequence of positive integers.\n\n**Operation**  \nWhile there exists an index $ i \\in \\{1, \\dots, |A|-1\\} $ such that $ a_i = a_{i+1} $:  \n- Let $ i $ be the smallest such index.  \n- Replace the subsequence $ (a_i, a_{i+1}) $ with $ (a_i + 1) $, reducing the sequence length by 1.\n\n**Constraints**  \n1. $ 2 \\leq n \\leq 2 \\cdot 10^5 $  \n2. $ 1 \\leq a_i \\leq 10^9 $ for all $ i \\in \\{1, \\dots, n\\} $\n\n**Objective**  \nCompute the final sequence $ A' $ obtained after no consecutive equal elements remain.  \nOutput:  \n- $ k = |A'| $, the length of the final sequence.  \n- The sequence $ A' = (a'_1, a'_2, \\dots, a'_k) $.","simple_statement":null,"has_page_source":false}