Christmas Streak 27/88: I've Run Out Of Ideas

When we multiply big numbers, for example $95\times37,$ the most common way of doing so is the method below:

$\begin{array}{cccc} &&9&6 \\ \times&&3&7 \\ \hline &6&7&2 \\ 2&8&8& \\ \hline 3&5&5&2 \end{array}$

The cryptogram below uses the same multiplication method as above.

Solve it and submit your answer as a six-digit integer $\overline{\color{#D61F06}N\color{#EC7300}O\color{#CEBB00}I\color{#20A900}D\color{#3D99F6}E\color{#69047E}A}.$

$\begin{array}{cccc} &&\color{#D61F06}N&\color{#EC7300}O \\ \times&&\color{#CEBB00}I&\color{#20A900}D \\ \hline &\color{#3D99F6}E&\color{#69047E}A&\color{#EC7300}O \\ &\color{#D61F06}N&\color{#EC7300}O& \\ \hline \color{#CEBB00}I&\color{#3D99F6}E&\color{#20A900}D&\color{#EC7300}O \end{array}$

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This problem is a part of <Christmas Streak 2017> series .